Get inside the character's mind and tell how the character feels about himself, other characters, or situation of the scene.
To give you one example, you could get into Hamlet's mind at the start of scene 2 with the court scene. If you keep in mind what you learn in scene 1, that Hamlet's dad has recently died, and then listen to the Claudius's first speech, you realize how unusual the current situation is -- his uncle is on the throne AND he is married to Hamlet's mother. That is strange and uncomfortable situation for Hamlet.
I would really think about what we learn about Hamlet from his first line. If I were the actor, my tone would be quiet and just barely concealing my complete disgust for the fact that the man who was once merely an uncle is now my step-father. The line also shows a quick wit. "A little more than kin (meaning closer than before) and less than kind (referring to the fact that he married Gertrude which seems rather unkind to the memory of his brother.) It is important to note too that the first line is an aside, so it is important to nail the tone so that the audience immediately has a sense of how Hamlet feels about Claudius.
The next line should be delivered with a kind of false cheery ironic tone. "I am too much in the sun." He is also showing his wit again with the pun on sun/son. He is too much closely related to Claudius now and is attempting to use verbal irony to contradict that the clouds of mourning hang on him.
When he talks to his mother about his state of mourning, I think he probably uses an earnest tone of voice to try to explain himself. He wants her to know that no matter how he looks on the exterior, he will be mourning on the inside. She seems to understand his point.
As Hamlet listens to Claudius talk about how he should get over his mourning for his father, Hamlet needs to convey his frustration through his facial expressions, posture, hand gestures, pacing/movement etc. I would have Hamlet rolling his eyes and/or avoiding eye contact. I also think turning away from Claudius when he is especially rude would effectively show how he feels. When Claudius says that the continued mourning is "obstinate condolement [and] a course of impious stubbornness," Hamlet has to show some anger/frustration with insults like that one.
I think that his telling his mother that it is because of her that is staying at Elsinore should made clear as a rebuff of Claudius. This could be accomplished with tone of voice and physically turning away from Claudius and towards Gertrude, perhaps even taking her hand or some kind of outward gesture.
The next part of this scene is Hamlet's first soliloquy. Here, he gets to unload all of the pent up feelings he had in the previous conversations. He can express his despair at the loss of his father; the disgust he has for the marriage of Claudius and Gertude; and the mix of disappointment and anger he feels towards his mother. This speech needs to be looked at very carefully for shifts in tone, so that the appropriate feelings are conveyed.