A good way to both understand and teach the serve is to think of it as consisting of two jobs, or two halves that make up a successful whole, as seen below in the formidable serve of Marat Safin.
Half one throws the racket head at the ball, whilst the job of …
Half two is to put the ball in the perfect spot to enable this to happen.
Job One: The Racket Throw
If your intention was not to hit the ball, but to throw the racket as far away from you as possible, then the best technique – to achieve both height and distance – would be similar to that used by Marat Safin here.
In 1 thru 5 (below) the racket head is swept back as the serve gets underway.
In 8 thru 10 his arm bends, so his racket head can drop, flop, or extend loosely down his back.
In 10 the elbow leads a loose arm, as Marat looks to throw up for height and distance.
In 11 the thrown racket has followed the elbow’s lead and Marat has launched himself up and into the throw.
The force of the thrown racket will (sorda) pull Marat along with it, as he makes no effort to halt the advancing racket head.
Having unleashed his throw, he will let it go where it will and the right side of his body will follow his thrown efforts, to further accommodate the journeying racket head (uber-speakers might need to read the last sentence a few more times).
Next step is to put a ball in front of the thrown racket face, and we have something like a serve.