Without greenscreen, there are two basic ways to clone. The first is splitscreen, which you mentioned. The second, is to use masks to manually cut the person out of the video frame-by-frame, so they can then be added into a second video. The second method involves a lot more work and time.
With ANY method of cloning, it is critical that you make sure the lighting match from one shot or element to the next. This is equally true of split screen or greenscreen shots. If the lighting in all the pieces doesn't match, you won't get a convincing result. So make sure the lighting doesn't change between the first and second shots of your splitscreen. Often, this means you either need to film the scene inside, where you can have full control over the lighting. If it has to be filmed outside, then you may need some decent lighting tools to make sure that the light is consistent. This could be powerful lights, or a very large shade.
Here are a few of the cloning tutorials already available in this forum, which a quick search of the Tutorials Forum for the word 'cloning' brought up:http://fxhome.com/forums/viewtopic.php?t=39833&highlight=cloninghttp://fxhome.com/forums/viewtopic.php?t=25753&highlight=cloninghttp://fxhome.com/forums/viewtopic.php?t=39119&highlight=cloning