Even though Yusuke may seem tough and dangerous, he's really a nice guy. In the beginning of the show, he saves a child from being hit by a car and is hit himself. He had warned the boy not to play so close to the road and then he started to make strange faces at him. ^_^ It was really cute. The child didn't listen though. After Yusuke had walked away, he started to play near the street again. Yusuke saw him go after his ball that rolled into the street and then Yusuke saw a speeding car coming. So he pushes the child out of the way and was hit. Well, not even the Reikai (Spirit World) thought he would saved the boy so they weren't ready for him. The were expecting the child to die.
Botan ("Death") told Yusuke that he had a chance to be ressurected because of this mistake. At first Yusuke didn't want to come back to life. He thought nobody would miss him because nobody cared about what happens to him. So Botan told him to go to his funeral and then give her his decision. So he did. At his funeral he saw how many people were upset that he was gone; Keiko, his mother, even Kuwabara Kazuma were upset. So Yusuke decided to come back to life.
Botan took Yusuke to see the prince of the Reikai, Koenma. Koenma gave Yusuke a special egg for him to hatch. The egg can tell whether a person is good or bad. If the person is good, the egg will hatch into something harmless; If the person is bad, the egg with hatch an evil monster that will devour him/her.
As Yusuke was waiting for the egg to hatch, Botan told him that he had to make sure his body wasn't burned in the funeral fire otherwise he couldn't come back no matter what. So Yusuke had to take over Kuwabara Kazuma's body and tell Keiko to make sure his body is safe. So she does. (Sorry, I could go into a lot more detail but I'd be writing forever) Anyway, one day an arsonist set Yusuke's house on fire. Well nobody was there and Yusuke's body was close to getting burned to ashes, but Keiko went into the house and saved him. She would've been caught in the flames too but Yusuke used the egg's energy to make a pathway for her. But now Yusuke can't be ressurected anyway because the egg is gone.
Soon after, Botan tells Yusuke that Koenma is going to ressurect him anyway. Koenma told Botan that is was a good thing the egg didn't hatch because it was going to be a monster to devour Yusuke.
Yusuke was ressurected and got his "Breath of Life" from Keiko. He still had to have his trial though and Botan came to him with the news that his "trial" was that he had to become a Reikai Tentai (Spirit World Detective). He wasn't too thrilled about it but he really didn't have a choice.