Why does Hamlet delay?

Hamlet is famous for being indecisive about killing Claudius to avenge his father's murder. As the play shows, he has sound reasons for not rushing into the castle and stabbing Claudius the moment his conversation with the ghost is over.
First, Hamlet has no way of knowing whether the ghost really is his father or if it is an evil spirit sent to lead him astray. He is wise to try to figure this out before he strikes. If the ghost really is an evil spirit, Hamlet will have murdered an innocent man. Not only would he have robbed a good person of his life, but he will have put his own soul in danger of judgment and hellfire after he dies. Therefore, Hamlet does the logical thing. He stages a play that reenacts the crime as the ghost described it. He watches for Claudius's reaction. When Claudius shows guilt, Hamlet has confirmation that the ghost told the truth.
Hamlet still delays. This time he does so because he sees Claudius alone at his prayers. He doesn't think it will be true vengeance if the praying Claudius dies in a state of grace and goes straight to heaven. Unfortunately, Hamlet fails to realize that Claudius is not in state of grace but actually thinking at that moment about how he doesn't repent for his murder.