The two-seamer is designed to move a little more than a four-seam fastball.
Grip the ball along the seams, at the part of the ball where the seams are closest together, with your middle and index fingers and put your thumb under the ball, in the smooth area between the narrow seams. Exert pressure on the ball with your middle finger and thumb.
A two-seamer is gripped a little tighter and deeper in the throwing hand than the four-seamer.
If you're right-handed, the ball should dive inside on a right-handed hitter. Vice-versa for lefties. A pro right-handed pitcher typically wouldn't throw this to a left-hander because the pitch would probably cut right into the barrel of the bat.
