The primary way to get the disc to fly in one direction or the other is to throw either backhand or forehand. Each throw gets the disc spinning in different directions (backhand = clockwise / forehand = counter-clockwise) so when it's flying through the air, it wants to glide right or left.

The angle at which you release the disc also greatly impacts how the disc is going to fly through the air, and you can easily make a backhand throw fly in the "wrong" direction with a little angle control.

The shape of the disc mold also really matters, and some discs will fly further or curve more than others. There are thousands of different discs made by different manufacturers with different plastic blends that all fly a little differently.

It's truly something to behold.