If you have just an automatic camcorder (with no manual controls) you won't be able to do it successfully.
If you have a camcorder which
does have manual controls, you can easily do it (..I use this technique for 8mm, 16mm and 35mm films).
1. Mount the camcorder securely alongside the projector, so that it's looking almost exactly along the same "line of sight" to the screen as the projector.
2. Set the camera's 'white balance' to the electric light bulb symbol, to match the kind of light which the projector lamp emits. If you have a manually-choosable WB setting, just turn on the projector - with no film in - and set the WB to match the 'white' of the light which the projector puts on the screen. (Don't run the projector for more than a minute with no film in it unless you take out the projection lens; the lamp's heat through the lens can liquefy any glue which holds any separate glass lens elements together.)
3. Set the camera's shutter speed to a speed
slower than 24 (if your projector's speed is 24 fps). So use a camera shutter speed of, say, 12. (..This blends together the individual frames shown onscreen, and thus gets rid of flicker.)
4. Run some film through the projector, and adjust the camera's
aperture setting, so that a normal section of the film appears to be the correct brightness in the camera's viewfinder or fold-out monitor screen. Then adjust the camera's
focus so that the film looks as sharp as possible. Zoom the camera's lens so that its viewfinder/monitor shows the very edges of the projected picture on the screen. Then shoot about 10 seconds worth of video.
5. Replay what you've just shot, and it may show you something
beyond the edges of the film and screen, because a camera viewfinder typically shows slightly less than what its lens captures. If you're going to eventually show the movie on a normal TV with a tube, this probably won't matter, as the picture will spill beyond the edges of the TV tube anyway. But if you want to watch the video on a computer or flat screen (..plasma/LCD/DLP..) TV, try another test shot after zooming in slightly. Replay again, and if you see just the edges of the film/screen, but no further, then you've framed it just right.
6. You've now set up the camera angle, white balance, shutter speed, brightness, focus and framing correctly. If it's a silent film, you're all set to start shooting your film from the screen. If it's a
sound film, you'll need a cable to run from the projector's audio output to your camera's audio input. TURN THE PROJECTOR'S SOUND DOWN VERY LOW, because connecting from a projector's loudspeaker output to a camera's
microphone input can distort the audio and wreck (..overload..) the camera's circuitry. If there's a mic volume control on the camera, turn it way down. To set the audio level, keep the projector's audio output fairly low, start the camcorder with the mic input turned way down, and every four seconds turn it up a notch. Play back what you've recorded; at first you may hear just hiss, but the sound should get clearer every four seconds. Choose the setting which sounds best without too much hiss or distortion. If you still get too much hiss, raise the projector's audio volume a little, and test again till you can't hear hiss, and you get good, clear, undistorted audio.
7. Rewind the film: you're now ready to shoot!