My cousin's son is a whiz at pretty much all of the Rubik's Cube variations... I can do the 3x3 one in a few minutes. I start out with the top edges, go to top corners, and then use a certain sequence of moves to do the middle and bottom edges at the same time. If I'm lucky, the bottom corners will line up for a multiple of that same sequence of moves to organize them into place, otherwise I restart from the bottom or one of the sides based on the configuration of the bottom corners, and repeat. Usually within a few times of doing this, I can get the bottom corners to line up and finish the cube. It's kind of a trial and error mixed with some memory of what works after a certain point.