Editing videos recorded using shadowplay

How is it done and with what software?

Well the video file is just MP4 so you can use any video editor to edit it like Adobe Premier, Final Cut Pro, Windows Movie Maker etc.

Rather than make a new thread I'll ask here are there any open source video editing suites out there?

I use Premier.

Here is a list of free and open source video editiors: http://en.wikipedia.org/wiki/List_of_video_editing_software#Free_and_open-source

The only one I have heard of personally is Blender no idea if any of them are good features wise, but if its just simple editing maybe they will be just fine.

I've been using Pinnacle 17 for a bit now an love it. The interface is easy enough to use for an amateur, but granular enough to for pro-like edits and movie making. 

My friend has Sony Vegas but he says that it wont work. any reasons why?

Get a codec pack

I use sony vegas pro 12 and it works fine