The grip for a tomahawk throw: two-finger grip. Squeeze the disc between your thumb and your index and middle fingers. These two fingers should be placed along the rim of the disc.
The grip for a thumber throw: hold tight while your thumb faces forward and runs along the inner lip of the disc. The run-up should be smooth; stop on your left foot and release into the air!
Watch this short clip from disc golf expert, Dave Roper from the University of Utah, for proper technique.