Draw a storyboard that shows what shots will go on the left and right sides of the screen. Pay attention to how you want the shapes and colors of both images to go together.
Record your video footage, composing your shots so that all of your action occurs either on the left or the right half of the frame. Anything outside this area will be cropped out later.
Import the footage into your favorite multi-track video editor and place the images on separate tracks. The top track will be the left side of the split screen while the bottom track will be the right side.
Crop the top video track so that its right edge is at the center of the screen. Move and re-crop as necessary to perfect the framing. The area that you cropped will now reveal the layer below. You now have a split screen movie.
Drag the rest of your footage onto the separate tracks in the order of your choosing. Use the standard editing tools to tweak edits and coordinate your cuts between the two sides of your split screen.