The hardest shot to master. Expect it to take at least 4-5 months of 3x weekly practicing before you feel any comfort with your serve. You just have to hit thousands of serves because it is not a movement done in any other part of your life.
There are many components to a good serve, and you must start with the basics, layering on additional components only when you can do the basics without thinking.
Here is what I would think about.
1) Proper grip. You want to use a proper serving grip, not some pancake paddycake loser grip. You’ll see this all the time with recreational players who only care about serving the ball in. But this means they will always be stuck with a lame serve. Every time they do it wrong, they’re hammering in bad habits. So you want to start with the harder to learn, but proper grip.
2) Point your left toe at the right net post. Your right foot should be about 1-2 feet behind your front foot.
3) Shoulders should be turned, so that if you were to draw a line from your back shoulder to your front shoulder, it would extend towards the right net post.
4) Shift your weight onto your back foot, then back to your front foot.
5) Toss the ball, directly above your head. An ideal toss would land slightly inside the baseline, perhaps 2-3 inches.
6) As you have tossed the ball, reach up with your left hand to create shoulder rotation in the up-down axis.
7) Bend your legs, and continue to stretch up with your left hand.
8) Explode up with your legs and swing up towards the ball, keeping your head up.
9) Land on your left foot and recover quickly ready for your opponent’s return.
But if you are a beginner you’re never going to be able to do so many things all at once. There are too many moving parts. So you have to break it down at first and then build on your foundation. Here is how to do it.
1) Starting with the racquet behind your head, check to make sure you have the proper stance.
2) Toss the ball and reach up with your left hand.
3) Swing up and out at the ball, spinning it into the court. At first you will likely feel like you are only carving the very side of the ball due to your grip, and you can expect many balls to bounce on your side of the court, or go into the net headed straight left. To compensate, you must try to hit the ball very very high and off to the right of the court. Even try to hit the ball over the fence on the right side of the court in order to get it to spin into the service box.
4) Once comfortable with the above, incorporate an increased shoulder turn both sideways and vertically.
5) Increase your leg bend and hip bend. Practice exploding upwards at the ball.
For a very technical understanding of the elements of the serve, I found this article to be interesting and useful.