The Stop Shot
The most important shot on the table.
In diagram # 1, I have placed an object ball about a foot out of the corner pocket and the cue ball directly behind it about a foot.
Practice stopping the cue ball at this distance from different levels below center. Start just below center hitting it sort of firm. Then move down the cue a little further, as you move down you will notice that you will hit a little softer. I will explain the importance of this later. Practice this about 8 different levels below center. After you have this down, leave the object ball in the same place, and move the cue ball back another foot, and practice the same drill. Keep moving the cue ball back one foot until you get about 5 or 6 feet away from ball.
Diagram # 1

The Use Of Tangent Lines
Above I had you practice stopping the cue ball. The reason this is the most important shot on the table, is that all shape is based off it. If your cue ball is stopped when it comes in contact with the object ball it automatically will travel it's natural tangent line. That is the orange line in diagram # 2.
Here I show the cue by the side pocket and the cue where it will come in contact to make object ball. The line drawn directly between the two balls is the tangent line.
So in order to travel this line your cue should be stopped (no spin on it) when it hits the object ball.
Now Let's look At This A Few Different Ways.
If you wanted to shoot this shot and just wanted to travel a short distance along the tangent line, you would shoot really low and soft. If you wanted to travel a couple of rails, shoot higher on the cue and firmer. You should be getting the picture by now.
Lets say you had to break out the two balls on the rail, and you wanted to make sure that you hit the 8 ball. Well you know that if you travel the tangent line that you will just miss them. Just add a little follow english and break them out.
If you are playing 9 ball and you are shooting the 3, and the 9 is sitting in the corner just use a little draw english.
This is how you use tangent lines for shape, breakouts and safeties.
Diagram # 2

Practice Drill For Tangent lines
Place an object on the table where I have the 3 ball in dia. # 2. Then place the cue up around the side pocket as shown. Then take a piece of chalk a draw a tangent line like the one shown. Now practice moving your cue ball along this tangent line, stopping it in different places, for different game scenarios.