Before you take the time to learn the sequence, first ask yourself this question: Is your serve good enough to follow in?
Many budding players fly into the court only to find the return flying right past them. Others are caught in the embarrassing situation of having the ball rebound off their ankles. You must stay back at the baseline if your serve lacks the necessary speed, spin and placement to make a safe approach.
Your objective in following your serve is not to put away the first volley, so don't charge in recklessly. Try to keep your poise and you'll be able to play the approach shot with finesse. Great players are remarkable in the way they can sprint into the court and repetitiously take their first volley inside the service line. The "human" player sees these acrobatic skills and tries to imitate.
Please don't! The biggest error is to overrun your first shot. Take your time, and stop a few feet behind the service line using a split stop. There are 18 feet between the service line and the baseline: if you cover 12-14 feet before you split stop - you're doing well. The real test is whether you can make the first shot on balance.
In following your serve to the net, the first and last steps are the most important. The first step should be a rhythmical continuation of your serve. The sequence is right-left-right-split stop. The number of steps you take depends on the speed and spin of your serve. A medium pace serve will get you a little closer to the net while a fast serve will leave you making your split stop further away from the net. Your last step brings your feet about shoulder width apart with the balls of your feet landing at the same time (your shoes should squeak when both feet hit at the same time).
If the ball is returned below the level of the net, you must play the low ball cautiously. Take a long stride towards the ball, bend your knees and get your backside down. Try to keep the low volley at eye-level. However, if the ball is floating you can continue closing toward the net and intercept the volley inside the service line and play it more aggressively.
Good players learn to anticipate their opponent's return from the placement of their serve. They predict the direction of the return and position themselves accordingly. Generally, move to a spot which is equidistant between your opponent's two widest possible returns. It is usually wise to slightly favor the down-the-line return because it has a shorter distance to travel before it reaches you.
Remember that the closer you get to the net the more dangerous you become. You have more angle to hit the ball to.
Go ahead and start your serve and follow first in a doubles game because you have only 1/2 of the court to cover. To be able to serve and follow playing singles takes a much stronger serve and more mobility to cover more of the tennis court.