- how Hamlet changes during the play – this may be overviewed Act by Act by paying close attention to his dialogue
I think of Hamlet's changes as more of a wavy line--moving up and down--than abrupt turnarounds. After the Ghost speaks to Hamlet, he is steadfast in his desire for revenge, and then he wavers. He gets "proof" that Claudius did, indeed murder the king--and then he wavers. The soliloquies are, indeed, the evidence of those waverings.
The soliloquies are absolutely the key; for, they are what prompt Hamlet to action. Without them, Hamlet would not have the opportunity to analyze what he has seen and/or heard since it is through these self-debates that Hamlet rises to action. For instance, it is only after he speaks with the Fortinbras and marvels at how this noble prince is ready to sacrifice his life "for an eggshell" that Hamlet is spurred to act as Hamlet the Prince and defend the throne of Denmark against all corruptors.
By means of his soliloquies and self-debates, Hamlet establishes his own values, for as he tells Rosencrantz and Guildenstern, one must establish in one's own mind that which is right and that which is wrong:
There is nothing either good or bad, but thinking makes it so. (1.1.)
If you just review his major soliloquies you can see a transition in his thoughts. He starts out the play feeling very melancholy over the death of his father and the incestuous marriage of his mother and his uncle. In Act 2, his major soliloquy compares himself to the players, and again he displays his frustration over the marriage and his disgust with his uncle, the murderer of his father. He is angry with himself for not taking more decisive action against Claudius. In Act 3, he is at one his lowest points. The "To be or not to be soliloquy" questions the value of action and inaction; life and death. He wonders why people don't just end all the misery of life with suicide, but realizes that the fear of the unknown makes us cowardly and makes us continue on. The next major soliloquy shows a change in Hamlet. He is justifying his not killing Claudius in an act of prayer, but we see a willingness to act under the right circumstances. Once he sees Fortinbras's men heading off to fight the Polish for a worthless piece of land he to becomes more determined to do what he has to do and declares "my thoughts be bloody or be nothing worth!" That shows quite a change! He reveals his new understanding of life and death most clearly in Act 5 in his conversation with Horatio. Here he says, "there's a divinity that shapes our ends rough hew them how we will." He realizes that fate plays part in everything -- no one has absolute control. This frees him to realize that all he can do is the best he can: "The readiness is all." This attitude allows him to go into the sword fight with Laertes ready for anything. Unfortunately, the attitude doesn't save him, but he is at least able to avenge his father's death.