Sirius Black is the son of Orion and Walburga Black, a descendant of the "Noble and Most Ancient House of Black." At Hogwarts, he was in Gryffindor House and a Marauder with James Potter, Remus Lupin, and Peter Pettigrew. He is Harry Potter's godfather.
Between being an unregistered Animagus before graduation, being one of the Marauders, and spending a decently long stay in Azkaban, he can safely be said to have a fairly low opinion of the law and similar regulations. He's brash, arrogant, and not quite as good as he thinks he is — attributes that lead both to Lily and James being found by Voldemort, and to his eventual death. If his ego is smaller than the land mass of China, you're looking at either a very major amount of character growth, or some serious OOC.
While he's unique in managing to retain his sanity despite a stay in Azkaban, he spends much of the books greasy, malnourished, and showing lasting psychological harm from spending years fighting his worst fears. He's both high-strung and high-energy, a trait aggravated by his imprisonment and later hiding and which causes him to take unnecessary risks.
On the other hand, he's intensely loyal to his friends, brave as you'd expect from a Gryffindor, and skilled enough to almost make up for his pride. Despite coming from a lone family line of pure-blooded elitists, Sirius does not share the typical biases against wizarding children of Muggles, and expressing that had him kicked out of the family house and his name burnt from the records.
With the exception of Peter Pettigrew (who he'd have quite liked to kill after the end of the First Wizarding War), Sirius remained on reasonably good terms with the other Marauders until (and even after) their deaths. As with the rest of the Marauders, his relationship with Severus Snape was not friendly, and tended to be more along the lines of outright bullying — in one case, Sirius almost got Snape killed by a werewolf. With the exception of one uncle, he did not get along well with his pure-blood obsessed family. He also treats his house-elf poorly, an attribute at odds with his philosophy that how a man treats his inferiors is a true sign of character.
His first encounters with Harry (which take place during Prisoner of Azkaban) were rocky at best; he appeared as a large black dog haunting Harry for most of the book. Toward the end, Harry almost killed Sirius in the mistaken belief that Sirius was responsible for the death of Lily and James Potter, and it was only due to Remus Lupin's interference that the truth was made clear. After that, Sirius's relationship with Harry was brotherly, and in many ways Sirius treated Harry as if he were James Potter rather than his godson.
Sirius can be caught up in some fairly bad slash, most often with Remus Lupin, but also with James Potter, Harry Potter, or Severus Snape. Expect some rather unpleasant squick and, in the case of the last two, one or both of the characters to go wildly OOC. (On the other hand, some slash involving him works out surprisingly well.)
Due to the nature of his death and his strong relationship with Harry, denial of Sirius' death or reversal of that death is frustratingly common, despite the effects on canon. Expect a replacement to kill.