I have a feeling JustDressageIt will be able to explain a little better then I can (or correct me if I'm wrong!) but here goes:
Turns on the forehand: Front legs stay in the same area, the back legs will step to the side (the inside leg will cross under his belly across the outside leg, and then the outside leg will step out). You can make a complete circle around but it's a slower calculated step by step movement, not a spin. You influence exactly when his leg steps.
Turns on the haunches: Kind of the opposite, front legs move and his back leg stays in the same area.
Shoulder-in: Instead of going straight, your horse moves along the rail in a straight line holding body a little diagonally (shoulder is more in the inside of the arena with his haunches on the rail) making 3 tracks with his feet instead of 2. Track 1: inside front, track 2: outside front and inside hind, track 3, outside hind.
Haunches in: kind of the same only with the haunches on the inside of the arena and shoulders on the rail.
Does that make sense? This is my "I ride dressage in brown tack" explanation.
Fortunately we had this amazing dressage trainer move kind of close by (she's a FEI trainer/competitor, USDF Bronze and Silver medalist and so incredibly nice!) and she comes to our barn to do lessons/clinics every other week. She's a little pricey but an incredible instructor.
You could also get on youtube and look up some of these movements to see what they look like. It's easier to see then explain. :)