I’m standing on the deuce side of the tennis court, getting ready to serve in a doubles match. As my partner stares ahead, the two women on the other side of the net look at me—and I just want to die.

You don’t need to be rich or already know how to swing a racket to get started with tennis. With a few smart choices, you can learn this trendy sport on a small budget — and have a lot of fun doing it ...