Best way to edit multi screen footage into one clip. I'm planning on making some "let's play" videos. These videos are usually edited together from screen recordings of multiple different players but have one shared audio track. 

Here's an example: 
                
             

What's the best way to go about doing this? What software would be good for this? Ideally I'd like to import all of the screen recordings into the software and then have a way of easily switching between "cameras". 

Links to tutorials doing this or something similar would also be a huge help.
Adobe Premiere Pro actually has a multicamera mode you can use where it will display all the videos playing together and you can switch between them.  You just line up the time and then can swap.  If they aren't time synced, then you can simply cut clips out and place them at will.  That's why it is called non-linear editing (NLE), because you can take clips and put them together without having to work linearly (deck to deck) like you used to.

While links are generally discouraged, I think this link to Adobe's help pages is probably the most ideal explanation of how to do multicamera editing.