Nuada was the king of the Tuatha de Danann when they first came to Ireland; in the Lebor Gabala Erenn it is said that he ruled for 7 years before the Tuatha De came to Ireland, was displaced when he lost an arm in battle, and then ruled a further 20 years after being healed (Macalister, 1941). Nuada was the son of Echtach, and had four sons Tadg, Caither, Cucharn, and Etaram the poet, as well as a daughter Echtge; no mother is mentioned (Gray, 1983). He is said in some sources to be married to Macha, one of the tre Morrignae, and he possessed one of the four treasures brought to Ireland by the Tuatha de, a sword which once unsheathed no enemy could escape and no wound from it could be healed (Berresford Ellis, 1987, O'hOgain, 2006; Jones, 2012). O'hOgain suggests that his name may mean "catcher" and theorizes that Nuada is the same deity as Nechtan and Elcmar (O'hOgain, 2006). He suggests this based on another name for Nuada being Nuada Necht, which O'hOgain believes is the earlier form of Nechtan; by this association Nuada would have been the original owner of Brugh na Boyne and would also possess the source of the Boyne, the well of Nechtan. Although difficult to prove with certainty this would reflect the strong connection to water seen in the related British deity, Nodens*. Other sources also suggest Nuada being the same deity as Nechtan and Elcmar, making him the husband of Boand who is cuckolded by the Dagda and then tricked out of possession of the Brugh na Boyne by Boand and Dagda's son from the affair, Angus (Monaghan, 2004). Based on this idea it would appear that after losing the Brugh to Angus Nuada moved to Sidhe Chleitigh, although alternate stories later claim his home to be sidhe Almhu or Slievenamon (Green, 1992; Monaghan, 2004; O'hOgain, 2006).
Nuada's most well known epithet is Airgetlamh, silver hand or arm. His name also appears as Nuadha, Nuadae, Nuadai, and Nuodai, with alternate spellings of his epithet as Aircetlaum (Gray, 1983). In the story of the Cath Maige Tuired Nuada was said to have lost his arm in battle, after which Dian Cecht, with the help of the smith Credne, fashioned him a new arm of silver that looked and moved just as a real arm would (Macalister, 1941). According to a note by Gray in the Index to Persons of the Cath Maige Tuired there is a story where Nuada's severed arm is carried off after the battle by a hawk (Gray, 1983). Because of this disfigurement Nuada was forced to forfiet his kingship, for the law of the Tuatha de stated that only an unblemished king could rule (Monaghan, 2004; Macalister, 1941). O'hOgain suggests, in his book The Lore of Ireland, that the original story of the loss of Nuada's arm may have actually involved an accident with his own sword, or even an intentional sacrifice, and that there may have been some connection to healing waters or even that his lost arm may have been symbolic of a river (O'hOgain, 2006). During the medieval period the story was expanded to include more details; it was his right arm that was lost in battle with the Fir Bolg warrior Streang (O'hOgain, 2006; Gray, 1983). Nuada was carried from the field only to return the next day with the request that Streang tie his own right arm to ensure fair combat - when Streang refused the other Tuatha de Danann offered a province of land to keep Nuada from risking his life in an unequal fight (Gray, 1983; O'hOgain, 2006). At this point Bres became king, but after 7 years Dian Cecht fashioned the silver arm, then his son Miach, possibly along with Ormiach, replaced it with an arm of flesh and Nuada took back the kingship beginning the secong battle of Maige Tuired (Macalister, 1941; Monaghan, 2004; O'hOgain, 2006). During the second battle Nuada gives the kingship to Lugh, who organizes the battle and fights the fearsome Fomorian Balor, who is Lugh's grandfather (Green, 1992). By some accounts Nuada ruled for 20 years after being healed, while others state that he and Macha died together in the second battle of Maige Tuired at the hand of Balar the Fomorian king (Gray, 1983; Macalister, 1941).
Nuada is a complex deity who can be seen as a god of battle, war, and also justice (Gray, 1983). Some sources also connect him to hunting (Jones, 2012). If weight is given to the parellels between Nuada and Nodens* and to the possible connections to Nechtan and Elcmar then he could also be seen as a god of healing and of the water, particularly rivers. The sword would be one of his symbols, as he possessed the sword that was one of the four treasures, and hawks may be associated with him. I personally have experienced the hawk as a symbol and messenger of Nuada, long before finding out the version of the story that connected him to the bird through the loss of his arm. Dogs and salmon/trout may also be associated with him, again if the link with Nodens and the Boyne is accepted. As Nechtan he would be connected to salmon through the salmon of knowledge that lived at the source of the river Boyne. Appropriate offerings would seem to be fish, and I have had sucess offering beer and Guiness.
Green suggests that Nuada's name may mean "cloud-maker" and suggests that his counterparts in other cultures include Nodens, Nudd/Ludd, and possibly the Germanic Tyr (Green, 1992). The arguments put forth to connect the deities etymoligically are reasonably sound, relying on the shared reconstructed Indo-European roots of 'noudont' or 'noudent' which means "to catch" and proto-Indo-European root 'neu-d' which means "to aquire" or "to utilize" (Nodens, 2012). However as with anything involving reconstructed language it is still only theoretical. There also seems to be a fairly strong mythological connection between these deities, particularly around the loss of an arm and replacement of the limb with one of silver. As I have reasearched this I have decided for myself that I am comfortable with O'hOgain's logic in connecting Nuada with Nechtan and Elcmar, and also the likely pan-Celtic parellels between Nuada and Nodens, Nudd/Ludd, and Noadatus. I am least comfortable with the connection to the Germanic god Tyr, although I can see the argument for an ancient root deity shared in common. Readers are welcome to draw their own conclusions.
*More on Nodens – also known in Wales as Nudd, or Llud Llaw Eirent (Llud the silver handed), sometimes equated to the Irish Nuada, and on the continent as Noadatus. Possibly a pan-Celtic deity synchronized with Mars, sometimes Silvanus, and in one case Neptune; his name may mean “Water Maker” or “Spirit of Water”, although it is equally likely to mean "he who catches" (Evans, 2011; Jones, 2012). A god of healing who had a shrine in Gloucestershire where votive offerings were made of bronze objects representing the area of the body the person needed to be healed, particularly limbs and eyes (Green, 1992). He is especially associated with amputees because he was believed to have lost an arm in battle, which was later replaced with a silver one, hence the epithet “silver hand”. His companion is a dog who can heal wounds by licking them; besides dogs, he is particularly associated with salmon and trout which may make good offerings to him (Evans, 2011).
Berresford Ellis, P., (1987). Dictionary of Irish Mythology
Green, M., (1992) Dictionary of Celtic Myth and Legend
Monaghan, P., (2004) Encyclopedia of Celtic Mythology and Folklore
O'hOgain (2006) the Lore of Ireland
Macalister, R., (1941) Lebor Gabala Erenn
Gray, E., (1983) Cath Maige Tuired
Evans, D., (2011) http://www.celtnet.org.uk/gods_n/nudd.html
Jones, M., (2012). Nodens http://www.maryjones.us/jce/nodens.html
Nodens (2012). Websters Online Dictionary. http://www.websters-online-dictionary.org/definitions/Nodens