Approach and Appearance
Within fairly broad parameters, everyone is doing the same thing when playing a theremin: moving the arm/hand/fingers toward or away from the antennae to create pitch and volume/articulation.

There are, however two other questions that are important to ask yourself, especially in the early stages of learning:

1) "What will I do?" (Put the emphasis on "I".)

From infancy we learn by watching and listening to others. We then make our own decisions, experiments, mistakes, etc. Do the same - watch and listen to all you can, try what you see, but apart from doing so, build in time to stop measuring yourself against others, particularly when first starting out – it will inhibit you in the long run. It's like deciding to learn to paint, and expecting a Van Gogh or a Rembrandt to appear on your canvas after your first try. Play for love, play for passion, play anything and everything, including just making noise. Your BODY is learning, your ears are learning, and your brain is actually creating new neural pathways that will help you immeasurably. For example: experiment with the volume antenna without consideration for pitch AT ALL (how radical!)-- find the absolute edge between silence and sound and try things extremely softy, or almost imperceptibly ease into notes, or working on sharp attack so that a when a note sounds it "bites" itself into existence. You owe it to yourself to make time to put aside what others do and find yourself. To approach your instrument as if you are going to TAKE CONTROL and consciously produce the "right" results for pitch, expression, meter, articulation, relaxation, listening, correcting, and turn it all into a song simultaneously is a recipe for frustration. It's why so many people give up. Take additional time to focus on allowing yourself to arrive at a comfortable APPROACH rather than insisting only on a perfect final result.

2) "What will OTHERS see?"

This might also translate as "what do I look like?" If you intend on performing in front of others, your playing appearance is important. Some theremin players I've seen very recently develop a glazed over stare that makes them look like zombies. Clara Rockmore's appearance was a cross between intense concentration and looking almost asleep – as a result the movements of her fingers and wrists draw more focus and are fascinating. There's some old footage from the 1950's TV show, You Asked For It, where the theremin player is so weirdly flamboyant with her volume hand that it's comical. Dr. Samuel J. Hoffman always seems to have had a somewhat bemused expression. All of those I'm mentioning play beautifully, and all had their own look. I've also seen a number of theremin players who seem to be wholly unaware of just how off-putting their expressions and personal idiosyncrasies really are. When I began, my children walked in on me one day and let me know that I was making facial expressions that they found bizarre, and that I, too, was staring in a way that they thought was scary.

If you watch close-ups of Clara Rockmore's face as she plays, you will notice here throat and tongue (her mouth is closed, though) are working – contracting, moving. (The movements of the mouth and eyes relative to developing new small motor skills that involve the fingers and hands is a subject too lengthy to get into.) The point is, that it's a good idea to give consideration to what you look like when playing, and develop an appearance that can be sustained and that keeps your AUDIENCE comfortable. They are the ones observing, and if the theremin player is glaring at them like something out of Night of the Living Dead while his pitch hand zooms around like a deformed claw, and his other hand looks like he's furiously swatting mosquitoes off the volume antenna it's going to be tough to watch and enjoy. The theremin player is more exposed than many other instrumentalists who can lose themselves totally in making their instruments function – hitting keys, pushing valves, plucking or bowing strings. But theremin players are playing the air, usually face-front, their arms and hands floating. Finding your own personal grace as you play is well worth exploring.