Preamble :
This method doesn't require Hollywood FX or any secondary video track. So, any Studio version can be used.
You probably have already seen this special effect on TV or in the movies where the same person appears twice on the screen, right? Take a look at what we can produce, with me and... me in the starring roles in my living room :
In fact, it's a very simple technique, I'll try to explain it to you in this tutorial. It uses Studio's 2D Alpha Magic transitions. You'll just need to place a camcorder on a tripod, film the scene twice with the person in the scene, but once on the left side of the set and once on the right side.
There's two important points to pay attention to, if you want the effect to be realistic : no item from the scene should move between the two videos. Moreover, the lighting conditions should be kept strictly the same. To avoid light fluctuations, it would be better to set your camcorder exposure to manual mode. As you can see in my video demo, I didn't pay attention to the the second caution and there is a slight light variation appearing on the tiled floor in the right part of the picture due to the subject sitting under the window.
Now, let's see in detail how to create this effect.
Step 1 : Create an jpeg image for Alpha Magic
First you open your favorite 2D picture editor (Windows Paint would be a simple example) and create a 720x534 monochrome picture half-white (255,255,255) and half-black (0,0,0), like this:

Save it as "Clone-NTSC.jpg" for example and place it in the Alpha Magic folder which should be at C:\Program Files\Pinnacle\Studio x\Alpha Magic for Studio 9-10-11, or C:\Documents and Settings\All Users\Shared Documents\Pinnacle\Content\Alpha Magic for Studio 12 and higher versions for XP and C:\Users\Public\Public Documents\Pinnacle\Content\Alpha Magic for Vista.
Bonus : You can download this picture included in the Clone.zip file available in the « Associated Files » section below
Step 2 : Import clips to Studio's timeline
Open Studio and import your two clips to the timeline:
The clip with the person on the left, to the left side and the right one just to the right side.
Step 3 : Select the new transition
After that, we will use the principle behind Alpha Magic files in order to be able to show off the two clips in the same time. Alpha Magic transitions rely on greyscale pictures. The complete white pixels (255,255,255) start first, while the complete black pixels (0,0,0) show at the end of the clip. The transition between one or the other follows the gradient in the greyscale image. When there's no gradient the two clips will be seen simultaneously. That's why we created clone.jpg. In the Alpha Magic Transitions Album you should find a new transition corresponding to your picture:

If you have any problem in finding the new transition, take a look at our tutorial "Tip-1 HFX effects do not appear in Studio". It also works for Alpha Magic Transitions.
Step 4 : Insert the transition
Insert the transition on the timeline between the two clips :

Step 5 : Lenght adjustment
The last simple step . . . . you lengthen the transition to the left so it covers the left clip completely:
In fact, the most difficult part is to synchronize the movements of the two subjects if you want them to interact in the rendered video. For that, it's a no-brainer : a little imagination, a good chrono, a few unsuccessful attempts, and a lot of patience should do the job.
Good cloning ! 
{Thanks to Loosecannon for the fine tuning}