Getting Started: The Four Most Important Points
 
If you are just getting started playing tennis, here are the four most important things to know about how to hit a tennis ball.

Controlling the racquet is the most important aspect of any stroke. Without racquet control, you never know what is going to happen when you hit the ball. 

The first step to controlling the racquet is to have your elbow in front of your body at the point of contact as seen in the figure below. In the illustration, the free hand of the player is holding the elbow of the racquet hand to demonstrate how far in front of the body the elbow needs to be, generally, but there are no fixed rules.
 
With your elbow in this position when you strike the ball, you will be able to maintain stability of the racquet and maneuver it in any direction.

When a pro tells you to hit the ball out front, they usually mean get the elbow in front of your body before you hit the ball.

The second most important point is to make clean contact with the ball. This is done by making the racquet move in a straight line just as you strike the ball. This idea is illustrated in the figure below.
 
The second most important point is that you must be able to move the racquet in a straight line for about 4 to 8 inches just as you are going to hit the ball.

The third most important point is that you must keep the butt of the racquet in front of the racquet head until you are ready to strike the ball. This is illustrated in the figure below.
 
Be sure to keep the butt of the racquet in front of the racquet head until it is time to strike the ball.

The fourth most important point is that you must keep the wrist laid back to assure control, clean contact, and power. The figures below illustrate the laid-back wrist for two grips, continental and western. This configuration is not only important at contact, it should be maintained throughout the entire stroke.