It's easy to do a "double exposure" effect -- but I don't think that's what you really want to do, Ralph. Doing a double-exposure effect will just make both characters in the scene look like ghosts, with 50% opacity.
If you're trying to make it look like a person is standing next to himself, you want to use the Chroma Key effect. To do this, you shoot your actor standing in front of a green screen and the "key" out the green so that you can place him into another scene that you've shot of him.
Similarly, you can shoot the person on the left of the scene and shoot the same scene with the same person standing on the right of the scene. When you combine the scenes, you crop each so that each takes up half of the video frame.
Either way works. It just depends on the effect you're trying to create and if the two versions of the actor are standing far apart or are right next to each other.
Based on my reading of the OP, I think that Steve's second method will be the one.
One strong suggestion would be to make sure that you use a good, sturdy tripod, and NOT move it between the two takes. Alignment will be critical to not having to do a ton of extra work. I'd go so far as to use "ankle weights" on the tripod to make sure that it's steady.
As a tiny twist to Steve's suggestion on the Crop Effect, if things are not 100% aligned, between shot A and shot B, you might be able to fudge it slightly with the use of Track Matte Keying, as you can "soften" the line between the the two shots.
Still, a very sturdy tripod and perfect alignment would benefit you greatly. Oh, did I mention a sturdy tripod?