This is a cry for help that comes up occasionally for acting teachers everywhere. I have a few thoughts about it.
Problems in the physical life of a scene invariably stem from a lack of clarity about the immediate potential future: more specifically, what you are looking for your partner to do and say next, but especially do. When problems pertaining to the physical life of the scene arise in class, I pose the question: what do you want to see happen next? Usually, the actor doesn't have much to say, thinks about it for a moment, and then comes up with something, but the something he comes up with is often lacking in HEAT or urgency, and it will often be of the form "I want her to say xyz". It may be true that xyz is what the actor in the scene wants to hear at that moment, but saying xyz is always a part of some larger development that will have a physical component, and getting clear about that is is the key to solving whatever is weighing down the physical life at that moment. Do you want to see the other person embrace you? Take your hands and dance you around? Leave the room? Leave the room with you? Sit down and confide in you? Once the actor has clarified this, then usually, without further ado, her body adjusts accordingly to prepare for the expected outcome. These are calculations that we make instinctively for ourselves in our own lives, but when we are pretending to be someone else, they don't always come as readily.
It's often important to be clear not only about what you want to see happen next, but what you are afraid will happen next, and what you may need to be ready to act to prevent. DO you need to stop someone from leaving the room? From picking up a gun? From leaving the bed? Clarifying these possible negative outcomes can have an equally clarifying effect on the actor's physical orientation towards the partner.
The actor is not sure what to do with his hands because he is not sure what he is waiting for or looking for to happen. She is so focused on the verbal interaction with her partner that she forgets that that verbal interaction is wrapped in a physical context. Usually, by reminding the actor of the nature of her physical engagement with her partner and her relationship to the space, her phsycal life sorts itself out.
If the actor is involved in a section of the scene where there is a back-and-forth discussion or debate or argument happening with another character, and they are in a kind of standoff, where they are confronting each other in a kind of deadlock, then there will naturally be some gesturing involved. When an actor is seeming or feeling self-conscious about these gestures, the answer is usually to clarify the desired or feared physical outcomes, as described above, and to remind the actor to consistently receive of his or her partner, which, most of the time, involves sustained eye contact. Tha partner's eyes, as I have
written about elsewhere, are the surest antidote to self-consciousness. I know this from firsthand experience. When I meet prospective students for coffee, I have a "spiel" that I do for them about the purpose of the class and the expecations involved. I have been doing this pitch for five years now. I typically gesture as I speak, to help make my points, the way that people who are explaining something typically do. However, I sometimes can feel a bit of self-consciousness about my gestures: I notice that the timing of the gestures relative to the words is off somehow, and I anticipate the gesture I will be making next, which distracts me. However, I have found that if I consciously look directly into to my interlocutor's eyes, not vaguely in the direction of the eyes but right into the pupils, unwaveringly though not aggressively, then the self-consciousness vanishes. There is some vulnerability in doing that, but it's worth it: my gestures then arise spontaneouly and line up perfectly with my words, I feel myself plugged into the "flow", and I am aware of all of this without being self-conscious about it. In other words, by fully giving myself over to connecting with my partner and communicating with her, I forget about what I look like and how I am being received, and I feel free. Or, as a wise person once said, the only way out is through.
Some people need to work to develop freedom in the joints of the arms. In his "advice to the players" speech, Hamlet warns about "sawing the air too much with your hands". If the actor has not discovered the requisite freedom in these joints, his arm will move monolithically, and he will seem to be sawing the air too much. The Alexander technique can be a great help with this, and studying T'ai-Chi is also enormoulsy beneficial in developing the expressive potential of the arms and hands.
In the end, it comes down to being in the moment. Paradoxically, though, being able to be in the moment successfully as someone else usually involves thinking things through.