How to put two videos into one side by side but playing at the same time?

Okay so I don't know if you've ever seen any videos by this guy on YouTube but his channel is called 'paint' i want to make a video like this >> http://m.youtube.com/...iU70KshcjA << where I put separate videos together but so they are playing at the same time. How can I do this either with a computer or even better is there an app for the iPhone that can do it?

Video editing software like Sony Vegas, Adobe Final Cut, or even Windows movie maker

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