Below are a general series of steps needed to accomplish a well-hit tennis serve. They basically apply to all kinds of serves.
1. As you take the racquet back, the inside of your hitting wrist and the hitting face of your racquet should point towards the court surface at the end of the take-back.
2. Push your front hip forwards as you move your weight over your bent front knee, thereby stabilizing your front foot.
3. The back shoulder must turn in to add its power to the hit as the racquet head is thrown up to meet the ball. It is very important to time the shoulder turn. Turning the hitting shoulder too early or too late will result in an ineffective tennis serve.
4. Keep your head up with your eyes on the ball at all times. At the hit the wrist should snap forwards to present the strings to the back of the ball, with an up, through and over action. Be careful not to baby this shot, so to speak. Hit the ball with authority.
5. During the follow through, let the racquet go past your left leg (or right leg, if you're left-handed) as your momentum carries you forward onto your right foot which has swung through across the baseline.