What is Hamlet's state of mind when the performance begins in Act 3 Scene 2 of Hamlet?
Such a loaded question! For some reason, my mind spun your question in a completely different way (so much so that I actually laughed when I read it). My first thought was, "People have been fighting about this since it was written, . . . and they still don't know the answer!" Namely, what exactly is Hamlet's state of mind after he says this:
As I perchance hereafter shall think meet / To put an antic disposition on. (1.5.171-172)
True, this is said far before Act 3, Scene 2, but it is important because some critics argue that, from that point on, Hamlet doesn't just act crazy, he actually goes crazy. This arguement is expecially significant because in the scene previous to the one you mention, Hamlet says this:
Go to, I'll no more on't; it hath made me mad, I say we will have no moe marriage. (3.1.148-150)
Mad in truth, or mad in jest?
To further the inquiry, at the beginning of Scene 2, Hamlet says some things to Ophelia that are quite unbecoming of a gentleman: things like "Lady, shall I lie in your lap?" while he shows signs of nervous tension like you've never seen. On the other side is the idea that Hamlet is obviously "acting" a bit nuts here, and his nervous tension is the result of the knowledge of The Murder of Gonzago plot: a plot that will surely reveal the truth behind Claudius' actions.
Therefore I must concur with the first answerer, the reader/watcher must infer Hamlet's state of mind; however, we may never know exactly how Shakespeare wanted us to feel about it because, luckily, this scene can be acted in completely different ways. Thus, the bard and playwright of the Elizabethan Age keeps things interesting for us centuries and centuries later!
Concerning Shakespeare's Hamlet, since this is a drama, state of mind is something a reader, for the most part, has to infer. Unless a character tells the audience what his/her state of mind is, in a soliloquy, for instance, state of mind is generally not something drama dwells on, although it is often revealed.
Based on Hamlet's plan to catch the king exposing his knowledge of how King Hamlet was murdered; his mockery of Gertrude and Ophelia; the bitterness he shows toward Gertrude and Ophelia; and his anxiousness to see the king's reaction, Hamlet's mind is probably anxious and excited, and filled with nervous energy.
In fact, Hamlet is like a cat waiting to pounce on a mouse--thus the title of the play, according to Hamlet when he is asked by Claudius what the name of the play is: The Mousetrap.
Claudius is the mouse and Hamlet is the cat: and Hamlet can't wait to pounce.