The grip on the seams of the baseball will determine the airflow around the ball while it is in flight. This will effect the movement of the ball on the way to the plate. The two-seam fastball will have more movement than the four-seam. To get the best sink or vertical movement on your fastball, the spin on the ball should also be vertical instead of horizontal. Vertical spin is the same as direct backspin.
Sidespin on the ball will create a flat plane while backspin will create a sinking fastball. The two-seam generally moves down-and-in to a right-handed batter when thrown by a right-handed pitcher and two-seam thrown by a left-handed pitcher generally moves down-and-in to a left-handed batter.
The two-seam will be responsible for many of the ground balls you will induce. It will also help the downward plane of your fastball. When throwing a fastball in a fastball count, more times than not, the pitch should be two-seams to promote movement.
Whenever you aim for the 2 Zone with a fastball, it should be thrown with two-seams. If you ask a hitter whether he would rather see a pitch in the middle of the plate that was straight, or one that had movement, every hitter would rather see the straight pitch.
One of the most important qualities of the 2 seam fastball is late movement. The later in flight the ball sinks, the less time the hitter has to react to the movement of the pitch. It doesn't take a lot of sinking action on the ball to move from the bat's sweet-spot to the bottom of the barrel, but it will take late movement.
If the pitch has big and early movement (horizontal spin) the hitter will be able to recognize the pitch earlier in flight, time the pitch easier, and match the plane of the swing with the plane on the ball. Strive for short and late movement compared to big early movement on the 2 seam fastball.