Start with the rod tip low, your casting arm extended, and your wrist in a tilted-down position. You’re going to lift the rod tip smoothly—enough to get the line moving—up-and-back. This is similar to the initial part of the backstroke pathway of an Overhead Cast. Keep moving up-and-back until the rod tip passes above head height, then immediately reverse direction by flipping your wrist upward and then snapping it back down again, ending with the rod low. Move your arm in the same general direction (up and then down) as the flip-and-snap sequence. The sensation and rod tip movement is that of a quick doubling back. The speed change as your hand flips-and-snaps through the double-back goes something like this:
The snapped loop will form out in front of the rod tip, and the line will be directed back toward you. As the loop reaches the end of the line, the fly will also flip back toward you (assuming all has been done correctly). The speed with which you make the initial lift and then the snap down will determine how far the snapped loop goes, and the angle at which you the make the snap will determine the direction of the cast.
A swift lift-and-snap can cast the fly cleanly behind you. A slower, less energetic lift-and-snap can allow you to cast the fly back to yourself. If you add some dedicated practice, you can catch the snapped leader or fly in your line hand. A Roll Cast, a Speed Pick-Up, or a Hand-Held Cast can be used to re-cast the fly.
The Snap Cast, with the myriad of small adjustments one can make to it, is a good place to just play around. See how variations in speed and direction affect the result and use what works best in the real world.