You can record many games directly with the Gear VR. Just pull up the menu (or set it up while in home by navigating the dash area) by holding down the back button and then navigating to and selecting the record video option. You can also set up livestreaming this way. A couple things to note is not all games can be recorded (the developer has to allow it, I believe), and you probably won't have any sound in the video.
Once you have it recorded, it's saved to your phone. Simply transfer it to your desktop/laptop and do whatever edits you want to do.
To get the game sounds recorded is a little trickier. I don't have time to go into ideas on that right now, but can later (need to head to the day job).
@
krisguy I believe "VR3" was a typo for "VR."