How did Hamlet stall the act of revenge in Hamlet? Provide examples.

The question of Hamlet's delay in avenging his late father's murder is a question critics have argued about for centuries. Why, if he knows his father was murdered by his uncle in the very first act of the play, does Hamlet wait so long to avenge his death? That's a difficult question to answer, although the other response to this question raises some good points, as does the link below. 

You are asking how Hamlet delays murdering Claudius, however, which is a different question. The first way Hamlet puts off murdering Claudius is by pretending to be insane. He does this to distract people while planning how to kill Claudius and confirming Claudius's guilt, as ghosts are not necessarily the most trustworthy source of information. When deciding to behave like a crazy person, Hamlet asks Horatio to keep quiet about the ghost, no matter

"How strange or odd soe'er I bear myself,
As I perchance hereafter shall think meet
To put an antic disposition on" (Act I, Scene 5)

Later in the play, as mentioned below, Hamlet delays killing Claudius by using the play within a play to determine if Claudius is guilty. He even asks Horatio to watch Claudius's face for any odd behavior. Claudius walking out of the play when he sees actions that were too close to his own should be evidence enough for Hamlet to believe Claudius guilty. 

Immediately after the play, Hamlet comes upon Claudius alone, in prayer. Again Hamlet delays, saying he would prefer to kill Claudius

When he is drunk asleep, or in his rage,
Or in th' incestuous pleasure of his bed,
At game a-swearing, or about some act
That has no relish of salvation in ’t—
Then trip him, that his heels may kick at heaven,
And that his soul may be as damned and black
As hell, whereto it goes (Act III, Scene 3).

After this scene, Hamlet agrees to go to England with Rosencrantz and Guildenstern, even though he knows this is part of Claudius's plot against him.

I must to England...
There’s letters sealed, and my two schoolfellows,
Whom I will trust as I will adders fanged,
They bear the mandate (Act III, Scene 4).

Hamlet clearly knows something is suspicious about this trip, but he goes on it anyway, postponing killing Claudius even longer. 

On his way to England, Hamlet sees Fortinbras of Norway waging war on Poland and thinks it's time to get it together and avenge his father already.

How all occasions do inform against me,
And spur my dull revenge! What is a man
If his chief good and market of his time
Be but to sleep and feed? (Act IV, Scene 4).

When Hamlet does finally return to court a few weeks later, however, he allows himself to get caught up fighting with Laertes and continues delaying killing Claudius. It isn't until the end of his duel with Laertes that Hamlet finally kills Claudius.