Hold the friggin' camera still.
I understand that a hand-held camera gives your movie more of an art-house feel, and judicious use of it during, say, a long chase sequence gives us the adrenaline rush of following our main character through the paces. Unfortunately, however, I just sat through an otherwise amazing film that I would have loved and raved about except for the fact that I spend half the movie noticing the camera work and feeling vaugely motion-sick. The hand-held camera is terribly, terribly overused now and unfortunately often so shakey that it looks like you strapped the camera to a poorly trained seal.
Excellent camera work should be like excellent make-up: it's so good you don't notice it.
There are devices that might help you; they're called a tri-pod or a camera dolly. I'm sure they're still in use in some movies. Please, find out what they are and start using them again.