Hamlet's character is plagued by indecision and inaction, which causes him to delay taking revenge for his father's murder. There are a number of examples, but three that I think would be the most important are:
1. At the end of Act I, Hamlet finds out from the ghost of his late father that he was in fact murdered by his brother. Hamlet had a hunch that this is what happened, but now he's got it from the mouth of the ghost himself. Yet, at the beginning of Act II, he decides to create a new ruse through the players, in order to make doubly sure that he would be acting correctly in murdering King Claudius. Hamlet states, at the end of his soliloquy in Act II scene ii: "The play's the thing wherein I'll catch the conscience of the king."
2. Hamlet has a chance to kill his Uncle when he catches him alone in Act III, scene iii. He doesn't however, because by doing so when he's praying, he would "this same villain send/ To heaven." This would not be revenge enough, so he decides not to do it.
3. Hamlet finally decides that "from this time forth,/ My thoughts be bloody, or be nothing worth" (IV.iv). The only problem is that when he decides this, he's being sent away to England. He's finally decided to do something about the revenge his father required of him, but he's going away from the target, under the target's orders.
These three elements of the play begin to illustrate the delays under which Hamlet operates.