It's not totally contrived to say that what you do with your other hand is more important than what you do with your racquet-wielding hand. Don't believe me? Then tell me how well the Sunday afternoon hacker plays - the guy who plays without changing grips, with his arm hanging awkwardly at his side, the guy who uses the windshield wiper volley technique, the guy who hits every serve at the level of his head, and picks up the balls with his hand.
Hold the racquet with the left hand. In a ready position, the other hand assumes all of the racquet's weight. This is as basic a fundamental as there is - since timing is primarily a function of relaxation, and it's unlikely to relax when you're squeezing the handle. (Hold it at the throat in your fingers, not the palm of your hand-like a water glass, with your fingers spread. I'm convinced that by spreading your fingers and relaxing your left hand and wrist, it serves as some kind of trigger, to relax the entire body.)
Change grips with the other hand. It's by taking the racquet back that you change grips. (Try it: with the racquet in a low ready position, simply draw it back with your left hand; by keeping your hand in a natural position, the grip will change automatically.)
Prepare with your left hand. For all strokes, it's the left hand that turns the shoulders. Keep the left hand on the racquet during the initial part of the backswing, and automatically, the shoulders turn. (Try it on the forehand; you'll be looking over your left shoulder to see the oncoming ball).
Stay down with the left hand. The left hand has a function on the follow-through--by keeping it down (and still), the player is less apt to lift up prematurely, and more apt to go forward. (It's a big deal, especially when trying to add pace, or handle pace).
Toss with the left hand. Of course. But after tossing, the left hand has a role--it stays up for a second, which improves the extension at contact. (And after contact, the left arm curls into the rib cage, which somehow facilitates racquet-head acceleration).
Relax with the left hand. When the point ends, slide your hand up the handle and get the racquet into the left hand. Then the hand, wrist, arm and shoulder can relax.