Now might I do it pat, now he is praying;
And now I'll do't. And so he goes to heaven,
And so am I revenged. (3.3.76-78)

In these opening lines of his famous speech in act 3, scene 3 of Shakespeare's Hamlet, Hamlet is contemplating Claudius's fate in the afterlife. "And so he goes to heaven" is a statement that reflects a widely-held belief during the Elizabethan period that a person's salvation or damnation (whether they go to heaven or to hell) is determined not by a "final judgment" of a person's behavior over the entirety of their life but solely by their state of mind in the final moments before their death.

Hamlet makes two references to this belief in this speech. One reference is in the lines cited above, and the later reference is to his own father's death, which he is now certain came at the hands of Claudius:

HAMLET. He took my father grossly, full of bread,
With all his crimes broad blown, as flush as May;
And how his audit stands, who knows save heaven? (3.3.82-84)

Hamlet's father was killed while he was sleeping, before he had a chance to repent his sins—for which he is now being punished in the afterlife. When Hamlet sees Claudius, he appears to be in the act of "the purging of his soul" and repenting of his sins at that very moment. If he kills Claudius now, Hamlet believes his soul will be sent to heaven.

It's not enough for Hamlet simply to kill Claudius for murdering his father. To rightly and fully avenge his father's death, Hamlet must ensure that Claudius's soul suffers as his father's soul suffers.

Thus, what seems at first to be another example of Hamlet's indecision and inaction could also be interpreted as very prudent behavior. Hamlet decides not to kill Claudius at that moment, but to wait until Claudius "is drunk asleep; or in his rage; / Or in the incestuous pleasure of his bed; / At game, a-swearing, or about some act / That has no relish of salvation in't" (3.3.91-94). In other words, Hamlet wants to kill Claudius when he's sinning, and send his soul straight to hell.

Hamlet tells himself that he can't kill the King while he is praying. But the real reason is probably that Hamlet can never make up his mind. Coleridge said that Hamlet "thinks too much." Hamlet sees too many sides to any question. When he does act, it is always on impulse, before he has had a chance to think. For example, he acts very courageously and decisively when his ship bound for England is attacked by pirates. Coleridge's diagnosis of Hamlet's character is probably the best that has ever been attempted. The answer by rishakespeare at this link below gives another perspective on Hamlet's actions. See what he says about "a harsh reality of an immoral world with his idealistic Christian reality."

http://www.enotes.com/homework-help/soliloquies-hamlet-385630

He needs to "catch" Claudius in the throes of some sin, so that he will die with an unclean soul, thereby sending him to Hell. He has just been absolved of (his brother's) murder because of his prayer.

Hamlet has had many opportunities to kill Claudius.  In fact, at this time period, revenge was justified homicide; Hamlet could at any moment of any day have walked up to Claudius and run him through.  Unfortunately, this is not in Hamlet's nature.  He reveals his hesitation in Act I when he says "O cursed spite, that ever I was born to set it right!"  His hesitations and trepidations lead to his circuitous plans - the crazy acts, the denouncement of Ophelia, and the altered play.  These get him nowhere, which is right where he wants to be. 

Of course, the moment is perfect when Claudius is praying.  Luckily, the intelligent Hamlet thinks of yet another excuse to avoid committing an act which is so out of his character.  Yes, he is praying, and yes, he will go to heaven.  So what?  The chance presented itself perfectly.  God allows for revenge.  Hamlet is only capable of killing Claudius when he, himself, is also dying. 

Hamlet doesn't kill Claudius at this point because he believes that Claudius is praying. He says that killing the king NOW would be "hire and salary, not revenge!" He simply cannot send Claudius to heaven, where he would surely go were he killed just after praying and purging his sins. He thinks that would not avenge his father's murder, because Claudius killed Old Hamlet without giving him the opportunity to pray, and therefore, Old Hamlet must spend time in hell. Hamlet thinks killing Claudius when he is fit for heaven would be like paying Claudius for the murder of his father. That simply would not do.

The real irony is that Hamlet does not realize that his revenge could have been complete if he had actually killed the king then and there, because Claudius was not really praying. Oh, sure, he was on his knees, but Claudius says that he knows he cannot be forgiven for the murder unless he truly repents, and repentance would mean giving up his crown and queen. So when Claudius says "My words fly up, my thoughts remain below./ Words without thoughts never to heaven go," he is really admitting that he knows he isn't forgiven. If only Hamlet had known, then Polonius, Ophelia, Rosencrantz and Guildenstern, Leartes, Gertrude and Hamlet all could have survived.

But then, the story wouldn't be a tragedy :-)

Hamlet doesn't kill Claudius at that moment because he thinks that Claudius is praying. Hamlet says that killing Claudius now would, "send [this same villain] To heaven” instead of Hell where he belongs. Hamlet vows to kill Cladius as Cladius had killed his father, and not send him to heaven.