When doing unit stills and on set, make good friends with the AD, but especially the boom op. You're going to be his shadow. He knows where to stand. Never get in the shots or cast a shadow into frame. Watch for it continually. You can usually stand next to a light, too, as long as you don't get in front of it.
You may be close to the mics, so don't make any noise. Wear soft shoes. Have access to a blimp, and even then, try not to shoot during really quiet times. Ask the sound guy to listen for the camera during a non-take. Realize that your angle is never going to be the best compared to the video camera, and make do with what you got. You might need to crank up the ISO a lot and process noise afterward, which is better than getting a blurry shot.
Don't ruin a take. Stay out of frame. Keep your sound, your body, and your shadows out of frame at all times.
You will need VERY fast lenses, usually primes, although some blimps can handle a 70-200 2.8 which is good, too. Always keep a 50 (or longer) 1.4 or 1.2 handy.
I've done unit stills for several small and one large production. It's interesting. Part of the job might involve making props that includes photographs, too, so get with the art department if it's needed.