I realise not everybody shares my interest in Nordic myths, but please bear with me...:)
Just to explain what Regin Smiður is all about. Grane was Sigurd's horse which was the descendant of Sleipnir, the horse of Odin (you can read more about it over here) . Regin the Smith was one of the three sons of the dwarf king Hreidmar, the brother of Otter and Fafnir. When Otter was killed by Loki, Hreidmar asked for weregild (compensation for the unlawful killing) and so Loki had to give him the treasures which he had stolen from the dwarf named Andvari.
However, the greedy king was still unsatisfied and Loki had to give him Andvari's magic ring which had been cursed by its rightful owner. As the result of the curse, Fafnir killed his father, took the treasure and ran away, without sharing with Regin, who swore revenge. Fafnir's love for gold caused him to turn into a horrible dragon and he spent day and night watching over his treasure.
Regin chose to live among mortals whom he taught all kinds of metalwork and he waited till finally he chose Sigurd as the instrument of his revenge. Sigurd promised to help but asked for a sword which wouldn't be broken in any battle. Regin made two swords, but Sugurd broke both of them easily. Regin then remembered about the broken sword of Sigmund (Sigurd's father) which he had received from Odin, and forged a new sword out of the remnants of it.
Sigurd killed the dragon and started roasting his heart for Regin, as the latter had asked him, but as he was testing whether it was ready he suddenly started understanding the birds' language and discovered that Regin was planning to betray him, thus he killed the dwarf and took the gold and the ring (which didn't bring him any good, but that's another story).
BTW, you can see where Tolkien got his inspiration:)