I'm soon going to be doing a music video with my friend.

However, I'm trying to do it a certain way. I'm going to record myself as one video and my friend playing an instrument as another video. Now I want to put these two videos today so that the are playing together at the same time in one screen.
You can see that it's done right here:
YouTube - "Just A Dream" by Nelly - Sam Tsui & Christina Grimmie

Can anyone help me achieve this? Is there a tutorial out there for this? Much thanks!
It won't be just two videos at the same time. It will most likely be about 3-4.
I have Sony Vegas and After effect.

Much thanks!