I drive three with my right hand only, and I sometimes lift my left a little bit when correcting or when they get out of pace. However, I can use my left as well to make the shuffle big(kind of like Ryo´s). This means both hands move at the same time, but the right is still heavily dominant. With a shuffle only driven by the right hand, you can very easily lift your left even higher to play with the shape, do three with a partner or move in to asynch. Synchpatterns usually end up in the middle of your body since the left is loose (unless your name is Trash ofcourse ).
I learnt my shuffle from taking down three high so gradually the pace would change. It seems to me that most people who get three high first learn synch, and people with wrap/stopoverstarts learn asynch (don´t know about that fact for sure though).
when it comes to learning three all you need to do is keep doing it. over and over and over and over and over and over again until you pass out from exaustion and then do it a hell of a lot more and you will create your own way of doing three.