In the Irish material we have the Tuatha De Danann as the Gods and we see the phrase "deithe agus an-deithe" Gods and not-Gods indicating a second group of beings connected to the Gods. Now to be fair people have been trying to explain who the an-deithe are for a very long time and there are lots of theories out there, including that they are the unskilled Tuatha De (based on the translation of Tuatha De Danann as People of Skill) and that they are the Fomorians. Personally I believe an-deithe refers to the daoine sidhe, the original inhabitants of the hollow hills and the ones who are most strongly associated with agriculture and the produce of the land. In mythology we see the Tuatha De and we also see references to the "Riders of the Sidhe". Now it's entirely possible that "Riders of the Sidhe", who appear in such tales as the Fate of the Children of Turenn actually reference the armies of the Tuatha De, but I tend to favor the idea that they are separate. To my own view it makes more sense that when the Tuatha De were in Ireland there were the an-deithe, the not-gods, in the sidhe (hollow hills), and that the two powers aligned much as the Norse Aesir and Alfar seemed to have done. Of course this is muddled by the fact that when the Tuatha De did go into the sidhe they came to be called the aos sidhe alongside the beings that were already there (in my opinion) so that some people today still believe the fairies are the Old Gods diminished, where I tend to see the Old Gods and the fairies as separate, with overlap. This confusion is added to by the fact that the Gods do have their own sidhe and are known to be active still, and the daoine sidhe, the siogai, the fairies, while clearly appearing in the folklore as not-Gods also live in the hollow hills and are active in the world. My own opinion is that the deithe, the Gods, are the Tuatha De Danann, and the an-deithe, the not-gods, are the beings known today as daoine sidhe or fairies, and that the two groups are inextricably linked, yet nonetheless distinct.
   The name daoine sidhe comes from the belief that these beings dwelt within the hollow hills, or that those hills served as entrances to their Otherworldly realm, sometimes called Fairyland or Elfhame. The daoine sidhe were equally likely to be connected to Otherworldly islands, usually seen in the west, which fisherman occasionally glimpsed out on the water but could never reach, as to the hills and mounds (McNeill, 1956). In Irish lore the Fair Folk live in the land, on the sea, and in the air, being associated with the mounds, stone circles, watery locations including the sea and bogs, caverns, and strange swirls of wind, as well as specific trees, especially lone Hawthorn trees (O hOgain, 2006). Looking at this we can perhaps begin to see that the Irish concept of an Saol Eile (the Other World) is as complex as the beliefs about the people (an daoine eile - the Other people, often referred to in English as the Other Crowd) who live within it. These Otherworldly lands are described as being fair beyond measure, beautiful, peaceful, and rich, and many mortals in tales who were taken into Fairyland did not want to leave it until a longing to see their families or old homes finally over took them. Generally when such people did leave the Fairy realm they would find that hundreds of years had passed and they themselves would die as soon as they touched mortal earth, because time moves differently in the Otherworld.
   The daoine sidhe are not, however, limited in any way to the Otherworld or to the area around the earthly entrances to their realm. In many stories they fare forth into our world, even appearing in mortal markets and fairs. Often they go unrecognized in such places, unless someone with the second sight sees them or they encounter someone who has previously dealt with them and still retains the ability to see them. In stories of borrowed midwives the midwife is often given a salve to rub on the new baby's eyes (usually after delivering the child from a local girl thought dead but actually taken by the fairies) and accidentally dabs a small amount on her own eye, only to have it put out later when she sees and greets the Otherworldly father at a public market. Likewise we see stories of the Fairy Queen riding out and finding - and taking - musicians who appeal to her, and the Fairy Rade is known to wander the world.
   Between the different fairy hills - of which there are many - exist fairy roads and paths which are invisible to mortal eyes and on which the Fair Folk travel; people must not build on these roads because to build a house on a fairy road inevitably leads to ill-luck and often death (O hOgain, 2006). To disturb the earthly site of the daoine sidhe's home was never a good idea either. Whether it was digging into a mound or cutting down a fairy tree, misfortune and possibly death was sure to follow (O hOgain, 2006). This belief is so pervasive and strong that to this day people will protest road planning if it interferes with known fairy trees or mounds.
     The daoine sidhe (also called the aos sidhe, both meaning people of the fairy hills) are often referred to with euphamisms like Good Neighbors, Gentry, Mother's Blessing, and Fair Folk; sometimes they are called fairies, which may be a shortened form of Fair Folk. In the older belief it was thought to be bad luck to call the daoine sidhe by that name (or any name using "sidhe") but interestingly this prohibition seems to be shifting to the term fairies, which of course was originally used as a way to avoid offending them. In modern practice many people have a strong prohibition against referring to them by any form of sidhe or using the word fairy, sticking instead to euphemisms (O hOgain, 2006). However in contexts like this blog or classes on the subject it is difficult not to use terms the majority of people are familiar with, so sometimes cautious compromises must be made. In some cases they are also referred to as wee folk or little people, likely something that began as a way to minimize their power or influence but has come to reflect a belief that their physical stature has literally shrunk.
    The daoine sidhe are described in some folklore as slightly taller than people and very beautiful, while other sources describe them as looking much like humans but with an Otherworldly aura about them. Generally the people of the fairy hills might be very pale and were usually finely dressed, but otherwise were very human-like in appearance (O hOgain, 2006). In folklore they often appear wearing green or grey, and may be blond or brown haired; they might be male or female and can appear alone or in groups. Among the Irish sidhe women were known to appear with messages or warnings, while groups of sidhe men would show up to play games of Hurling, for which they required a single human player in order to have the game (Yeats, 1966). The daoine sidhe were also known to ride outt in processions, called fairy rades, which could be dangerous to any humans they came across, although in the Ballad of Tam Lin we see a Fairy Rade offering an opportunity for a woman to rescue her lover from the fairies. The Fair Folk are often invisible to mortal eyes, unless they wish to be seen or the person has second sight, but their passing can sometimes be perceived nonetheless. The fairy host travelling may create whirlwinds or sudden blasts of wind called sidhe gaoithe or séideán sídhe (MacKillop, 1998). This ability to seem invisible relies on one of the Daoine sidhe's most well known powers, that of glamour, or the ability to deceive mortal senses by making one thing seem like another. Galmour is seen in almost all fairy stories where, for example, a desolate cave is made to look like a castle or a handful of leaves made to appear as gold coins. 
     As in the Norse both the Tuatha De and the daoine sidhe have been known to produce children with a human, although with the daoine sidhe they seem more likely to steal a bride from her wedding to marry one of their own number instead, who would later be helped by a borrowed midwife to deliver her Otherworldly husband's child. It is generally believed that the daoine sidhe have a low birth rate and need to supplement their numbers, which they do with human babies and women; they are also well known to take midwives and musicians, although those are usually released after a time back to our world. Those taken into Fairyland could not return if they ate or drank anything while there, unless they had been taken only for a pre-determined time period like Thomas the Rhymer. There are also stories of those who join the daoine sidhe for what they think will be a single night of dancing, in a fairy ring, or entertaining in a sidhe (fairy hill) and emerge at dawn to find that seven, 70, or hundreds of years have passed on earth. The Fair Folk were also well known for stealing cattle and horses that they fancied (O hOgain, 2006).
  The daoine sidhe are sometimes divided into courts, what the Scottish call the Unseelie and Seelie Courts, or loosely the Unblessed and Blessed Courts. The etymology is tricky on this one, but generally it can be said that Seelie is equated to good or benevolent, often seen in older sources in the phrase "seelie wights". McNeill refers to these as the Seely and Unseely, or good wichts (wights) and wicked wichts (McNeill, 1956). Wights itself is an older Germanic term borrowed into Scottish, which means, loosely, any supernatural being but can also be used to simply mean any being at all. In the Irish it is believed that fairies have white blood and that the two opposing courts sometimes battle at night, leaving otherwise inexplicable white liquid (fairy blood) to be found as evidence of these events in the morning (O hOgain, 2006). It is widely believed that the daoine sidhe are ruled by a monarchy, but they also encompassed a working class who might go to human markets in disguise or appear to human farmers seeking to borrow something (O hOgain, 2006). The Fair Folk ride on fine horses and are seen in the company of hounds; generally these animals are either black, white, or grey. In some stories it is said the deer of the forest are the cattle of the fairies (McNeill, 1956).
  In folklore the daoine sidhe are seen as being especially active on the quarter days, Samhain, Imbolc, Bealtaine, and Lughnasa. It was believed that on these days the fairies moved house, processing forth from one hill to another along set fairy roads (McNeill, 1956). Samhain and Bealtaine are the strongest times of fairy influence and so are times when great care should be taken to avoid running afoul of them (O hOgain, 2006). At Bealtaine it was believed that the Fair Folk might travel abroad, appearing as a stranger at the door asking for milk or a coal from the fire; to give either would mean giving the household's luck away for the year to come (Wilde, 1887). At Samhain the daoine sidhe are known to move from one hill to another, from their summer to winter homes, and it is quite dangerous to meet them on a fairy road that night (Estyn Evans, 1957). The Fair Folk are also especially active at twilight and midnight, and the slua sidhe, a kind of airborne malicious fairy host, is most active at night.
   There is a long standing and complex association between the Fair Folk and the dead, and indeed it is difficult to separate out the two groups in many cases. The dead often appear among the ranks of the daoine sidhe, especially the newly dead, and many stories feature someone seeing a thought-to-be-dead friend or relative in a marketplace. This is often explained by saying that the person had not actually died but was in reality taken by the Fair Folk and a changeling left behind, which was buried in the person's name (a common ploy with new brides and other attractive young people). The connection runs deeper than this though as the sidhe that the Fair Folk live in are often ancient burial mounds, such as Brugh na Boyne (Newgrange). In many fairy stories a person is believed to have died but appears, often in a dream, to a loved one and explains that they have been taken into Fairyland and can be rescued in a certain way, usually by the living person going to a crossroads at midnight when the Fairy Rade will pass by and grabbing their loved one from the horse he or she is riding (O hOgain, 2006; The Ballad of Tam Lin) Many people say that the Slua sidhe, the fairy host of the air, are spirits of the mortal dead (McNeill, 1956).
   Offerings to the daoine sidhe traditionally include milk, butter, and bread, left by the doorway or at the roots of a fairy tree, as well as a bit of whatever one is drinking poured out onto the ground (Estyn Evans, 1957). Additionally milk might sometimes be thrown in the air for the fairies or butter buried near a bog as an offering to them (O hOgain, 1995). At holy days it was also a custom to offer a heavy porridge which might be poured into a hole in the earth or bread which could be left out or tossed over the shoulder (McNeill, 1956; Sjoedstedt, 2000). The custom of pouring a drink out is mentioned in Irish Folk Ways, and is something I was familiar with as a family custom; my grandfather would pour out a bit of his beer in this manner, and while my father didn't, that I know of, I've long been in the habit myself of offering a portion of anything I am drinking outdoors to the Good People. It was also once the custom to bleed live cattle on Beltane and offer the blood to the fairies (Estyn Evans, 1957). In a modern context people seem to offer milk, cream, bread or other baked goods, honey, and portions of meals, as well as alcohol.
   The daoine sidhe can bless or harm people.  Fairy gifts could be good and lead to great blessings, or they could be illusions which would turn to leaves or grass at dawn. The sidhe gaoithe (fairy wind) which was a sign of the presence of the fairy host, could bring illness or cause injury (MacKillop, 1998). Elfshot is another well known fairy malady, a sudden pain, cramp, or stitch caused by an invisible fairy arrow shot into the body by angered daoine sidhe. Elfshot might also be used against cattle, who would slowly waste away after being struck (O hOgain, 1995). In many cases it was also believed that elfshot was a power given to witches, which they learned from the fairies - indeed many Irish and Scottish witches were thought to have learned both malediction and healing from the Fair Folk with whom they were believed to deal (Hall, 2005). In contrast though those who were considered friends of the daoine sidhe were often privy to special knowledge and taught things like healing and magic, or a musician might be given great skill (O hOgain, 2006). The daoine sidhe might appear as a stranger at the door seeking to borrow something or needing milk or a coal from the fire, alone in a field or wood, or might be encountered on the road; those brave enough to seek them out might choose to sleep on a fairy mound, knowing that the result would either be blessing or madness.
  There are a variety of protective charms against the Fair Folk, far too numerous to get into here, but I'll offer some examples. To keep a new mother and infant safe they would be given milk from a cow who had eaten mothan (McNeill, 1956). To get the host, particularly the Slua, to release anyone they may have taken one should throw the dust from the road, an iron knife, or your left shoe and say "This is yours; that is mine!" (McNeill, 1956). Should a person be suffering from the ill-willing attention of one of the fairy people a fairy doctor must be found, that is a person with special knowledge of the fairies, who can diagnose the exact issue, be it elfshot or fairy blast, and come up with the appropriate charm, chant, or herb to cure the person (Wilde, 1887). Tying a red ribbon on cattle or horses was thought to keep fairies away, as was tying a rowan twig on to a cow's tail, or lightly striking the animals with rowan or hazel switches (O h Ogain, 1995; O hOgain, 2006). Rowan and red thread is another well known protection, as is anything made of iron, a material that the Fair Folk cannot bear.
   Honoring and offering to the daoine sidhe is - or should be - an important aspect of an Irish polytheist practice. The Fair Folk have long been offered to and this is a practice that we would do well to continue in our thoroughly modern world, rather than turning our backs on the Otherworld which has so long existed side by side with ours. Honoring the daoine sidhe not only prevents ill-luck but can grant good luck and blessing and more importantly helps create a reciprocal relationship between us and the Fair Folk based in respect and friendship. It's never a bad idea though to know signs of fairy trouble as well and how to protect yourself against them, or in a pinch were to find a Fairy Doctor or bean feasa (wise woman) to help you. Humans have a long and complex relationship with the daoine sidhe - as long and complex as the history of the Fairy folk themselves - and they are just as present today as they have ever been. 

* the folk beliefs vary across Ireland in ways that can be contradictory, so that the tree that should never be cut and brought inside in one area, lest it draw the Fair Folk, is the same one recommended elsewhere to protect against them. Similarly one area might believe that keeping dirty water in the home draws fairies and grants them entrance while another area believes this water drives them away. This can make it difficult to say almost anything with absolute certainty as there are nearly always exceptions.

Further reading and References:

 Yeats, W. B. (nd) Celtic Twilight http://www.sacred-texts.com/neu/yeats/twi/twi39.htm
 Hall, A., (2005) Getting Shot of Elves: Healing, Witchcraft, and Fairies in the Scottish Witchcraft Trials.     
      Folklore, 116
Briggs, Katharine (1978) The Vanishing People: Fairy Lore and Legends.
Evans-Wentz, W. Y. (1966) The Fairy-Faith in Celtic Countries.
O hOgain, D., (2006). The Lore of Ireland
   --- (1995). Irish Superstitions
McNeill, M (1956). The Silver Bough, volume 1
The Sidhe, the Tuatha de Danaan, and the Fairies in Yeats's Early
          Works http://www.csun.edu/~hceng029/yeats/funaro.html

The Ballad of Tam Lin http://www.sacred-texts.com/neu/eng/child/ch039.htm
MacKillop, J., (1998) A Dictionary of Celtic Mythology
Wilde, F., (1887). Ancient Legends, Mystic Charms, and Superstitions of Ireland
MacDonald, L., (1993) People of the Mounds. Dalriada Magazine http://deoxy.org/h_mounds.htm
Estyn Evans, E.,  (1957). Irish Folk Ways
Sjoedsedt, M., (2000). Celtic gods and Heroes