We already know from Hamlet's conversation with the players that occurs in the Act 2 that he is planning to change "a dozen or sixteen lines" from the play The Murder of Gonzago. We assume that he is going to change some of the details of that murder-plot story line to better match what Claudius did to King Hamlet. Hamlet is relying on this play/plan to prove Claudius's guilt, so he has to make just the right changes.
These are a couple of things that are likely "changed" by Hamlet.
1. It is most certain that the method of the murder in the actual play would not have been poison poured in the ear. That is odd, but it IS what Claudius did, so Hamlet would have changed a more traditional poisoning (like a poisoned cup of wine) to this method of poisoning so that he could watch Claudius's reaction to the scene.
2. When he is asked about the title of the play, Hamlet says it is called "The Mousetrap," yet we know it called The Murder of Gonzago so that leaves us to consider the title and realize that Hamlet is joking that the play is a "trap" to catch Claudius's guilty conscience and Hamlet is like a cat "playing" with the Claudius, the mouse in this metaphor.
3. During the play, Hamlet likely added the lines about how the Player Queen vehemently protests the suggestion that she would ever marry again if anything were to happen to her husband, the player king. The Player Queen even says, "A second time I kill my husband dead / When second husband kisses me in bed." Hamlet wants to prick at this mother's choice to so quickly remarry after her husband's death.
4. Hamlet has the murderer be a "nephew to the king" rather than a brother to the king (like Claudius). This is perhaps to not reveal too much of what he knows.