Watch the Right-Hand Techniques online guitar lesson by Bruce Arnold from Guitar Physiology Survival Guide
In general the right hand should remain relaxed and most of the movement will come from your forearm with your elbow making small adjustments as you change between strings in some cases. The most common way that guitarists pick is with movement from their wrists.
While this can work and obviously does for many guitarists it is also a movement that can eventually cause carpal tunnel syndrome. By having the movement of the pick based in your forearm you are moving a part of your body in a way that it naturally moves, and using a larger muscle. This forearm movement is the same movement you use to drink a glass of water or screw in a screw with a screwdriver.
This forearm movement works equally well for picking and strumming. If you have already learned to play using your wrist then switching to your forearm can take some time. It is normal to feel very clumsy and out of control. Remember, your pick expresses rhythm in most cases so you need to transfer the rhythms you know in your wrist to your forearm. I will recommend a few exercises to do to facilitate this transition.