early life
Since LJ only gives us a few quick peeks into Stefan's life in Florence, there's not much I can say that isn't speculation. We do know that Stefan was born into the Florentine nobility in the 15th century. His mother died when he was very young, so it's likely that the biggest impact she had in his life was for her death to be the catalyst for his brother's resentment towards him. He studied with tutors in a variety of subjects, probably in his home. His father seemed to have been a rich and fairly important man in Florence, since Damon remarked to him that his "friends" were the people who fawned over him for money. His father's position probably held a lot of influence with Stefan since it was mentioned that he felt a duty towards Florence that was important enough for Damon to mention it to Katherine during an argument.

turning point
The turning point in Stefan's life came when a fair-haired girl from Germany came to stay with his family. They fell in love and she pulled him into a world he knew little about. We know that he had very little previous experience with girls, so his feelings for Katherine were very new to him. It was also through Katherine that Stefan was born into his life of darkness. When his brother Damon came home after quitting University, he too fell for her charms and Katherine began to divide her time between the two brothers. This caused Stefan a lot of pain and jealousy and ultimately led to both of them demanding that Katherine choose between them.
On the night before she made her choice, she came to Stefan's bedside and turned him into a vampire. As a result, Stefan went to the meeting place the next day quite confidant that his love had chosen him. When Katherine arrived, he found that she had changed both of them into vampires and had decided that she couldn't give either of them up. Rejecting this idea, the brothers walked off, sending Katherine off in tears.
The next morning, both boys went to her rooms to plead with her only to discover that she had killed herself so that she wouldn't cause any further strain in their relationship. Both brothers blamed each other and went for their swords, each killing the other in battle. They woke up in their tomb days later, and began their separate paths into the night.

a life of solitude
Stefan's life from the time of his mortal death until his move to Fell's Church is a bit of a mystery. All we know for sure is that he met Damon once or twice in Florence, and that he spent his life alone in grief outside the city walls somewhere. Such solitude grew tiring after a point, driving him to find a new life in Virginia...

present day, present time
Stefan moved to Fell's Church in hopes to put his former life behind him. There, he met Elena Gilbert and fell in love, only to find his brother there watching, coveting his girl again. But after a struggle leads to Elena's death and transformation into a vampire, the three team up to find the cause of the negative energy in the town.
It is now that a five century old lie comes to light. Katherine, far from being dead, lured the brothers to Fell's Church to punish them for ruining her plans of reconciliation after her "death." Elena breaks free from their captivity and sends Katherine unprotected into the sunlight, killing them both in the process. And here our dead hero is left alone to grieve again.
Months later, we meet the brothers again, this time trying to live together in Italy when trouble again befalls Fell's Church and they are called to help. Rushing to the aid of their human friends, they face Katherine's creator, an Original by the name of Klaus. Through a miracle, the spirit of Elena saves the town from Klaus, and she is returned to life as reward. Happy Ending.

Yes that was an extremely quick bio, but I didn't feel like retelling the entire story bit by bit.