In case you didn't know, "Sirius" is the name of the dog constellation. So it is rather unsurprising that his animagus form is a black dog.
At Hogwarts, he and his best friend, James Potter, were record breaking trouble makers, rather like Fred and George in that sense. Unlike Fred and George, Sirius was also a good student. He managed to become an animagus in his 5th year at Hogwarts.
After they finished school, James and Lily Potter were married, and had a son, Harry. When it was suspected that Voldemort was going to try to kill James and Harry, the fidelius charm was performed, and Sirius was made secret keeper. He soon changed with Peter Pettigrew, who promptly betrayed Lily and James to Voldemort. And Voldemort... and Voldemort... *whispers* killed them *sniff*
The same night that Lily and James were killed, Sirius had planned to check on Pettigrew at his hiding place, but found him gone. Suspicious and worried, he rushed to Godric's Hollow (James and Lily's house) and found everything destroyed, and James and Lily dead.
Horrorstruck at what Pettigrew had done, he set off after Pettigrew, giving Hagrid his flying motorcycle to get baby Harry to his Aunt and Uncle's house. When he had finally cornered Pettigrew, he faked his own death and framed Sirius, who was then given a life sentence in Azkaban without a trial.
After 12 years in Azkaban, Sirius found an article in the newspapers - with a picture of Pettigrew (in his animagus form, a rat). The article stated that the boy who owned him would be going back to Hogwarts, where Harry Potter was. With the thought of Pettigrew's ability to kill Harry, Sirius found the strength to break out of Azkaban.
He made his way to Hogwarts, first stopping at Privet Drive to glimpse Harry, and nearly causing him to be run over by the Knight Bus. He eventually made it to Hogwarts and made friends with Hermione's cat, Crookshanks, who tried to help him catch Peter Pettigrew aka Scabbers. In the end, he managed to lured Harry and Hermione into the Shrieking Shack by taking Ron hostage.
Harry got into a position to kill him, still believing that Sirius was the one to have betrayed his parents over to Voldemort. Luckily for him, (you figure out which one), Remus Lupin arrived on the scene in time to prevent this tragedy. Sirius told Harry what had happened, but he didn't believe him until he transformed Scabbers back into his human form, Peter Pettigrew.
On their way back to the castle to hand Pettigrew over to Dumbledore and the Ministry of Magic, however, the full moon came out from behind a cloud and Lupin turned into a werewolf, and Peter escaped and fled, leaving Sirius without any proof of his innocence. At this point, the Dementors guarding the castle came out from their posts and attacked Harry and Sirius. They were saved by Harry (from the future), who was using a time turner to get back to the past.
Sirius was then taken by Snape to the castle to be handed over to the Dementors to be given the kiss. He was saved by Harry (using the time turner), and escaped on Buckbeak, the hippogriff.
Sirius also happens to be Harry's Godfather, and spends most of the fourth book worrying about something terrible happening to him. At the end of the 4th book, we're left with the knowledge that he's gone to Lupin's house, and that they're going to find their old friends to do something about Voldemort's return.