Tetherball Tactics
In tetherball, as in many other sports, gaining and keeping control of the ball is the key to winning. The obvious way to keep control of the ball is to hit it over your opponent's reach each time it comes around, but many less obvious tactics come into play at more advanced skill levels.
Stealing the Ball
One of the most valuable tetherball tactics is the sacrifice wrap. When a ball approaches from your opponent's hit that is too high or awkwardly angled for you to hit back over her easily, your best choice is often to hit the ball once in her direction, setting yourself up for an easy hit in your own direction. After you sacrifice the wrap, move forward in your own half to take the offense. One wrap is usually insignificant in comparison to gaining control of the ball.
When you're on defense, trying to steal the ball, you need to keep moving forward and back within your half. If you stay in one spot, 
your opponent will be able to set up easy control of the ball by making it travel in a circle that tilts just enough so that its lowest point is within his reach and its highest point is above you. If you move forward and back within your side, you will force him to constantly change the angle of his ball's flight and his position on his side. He will always want to be directly opposite you, halfway around the circle, but you'll have a good chance to steal the ball by suddenly rushing to a position closer to him. He will be hitting the ball so that it comes down to meet him wherever he is, and the nearer you are to that spot, the closer the ball will be to your reach.
Serving
If you play by the rules that allow the server to keep hitting the ball, the smartest serve will just pass once over your opponent, then provide an easy second, third, and subsequent hit until you've wrapped the ball. As I explained on the rules page, this makes it so easy for the server to win, it doesn't make sense.
Under the rules I prefer, the server must wait until the receiver hits the ball or the ball wraps four times before she can hit again. This makes serving a disadvantage, one that can be diminished only by thoughtful tactics.
If you have tremendous power, you can try to hit your serve hard enough that it will wrap four times before the receiver can reach it. This is extremely difficult, but if it works, you'll have an easy game.
For most servers, the smart play is to hit the ball at a sharp angle so that the plane in which it flies is tilted closer to vertical than horizontal. You'll probably get only one wrap out of such a serve, but the purpose is to prevent your opponent from getting a clean first hit. With the ball moving up and down on such an extreme tilt, you will easily see where it will come down to your opponent, so you can position yourself accordingly. If she will be making her first hit at the front of her half, you can rush her and jump up to block her hit. If she will be hitting from her back line, you can set up at your back line to try to intercept as the ball comes around. It's harder for her to pass you if you're almost a full circle away than if you're only half a circle away.
Hitting Techniques
When you do get a chance to hit an oncoming ball solidly, an unusual hitting technique often works better than the instinctive one- or two-fisted punch. 
Try hitting the ball simultaneously with the pinky-end pad of your dominant hand (like a close-fisted karate chop) and the palm of your other hand. This gives you the ideal combination of power and control.
When you have control of the ball, hitting with the fingers and palm of your inside hand is the best choice. You only need enough power to get the ball over your opponent once. As long as you can keep hitting it each time around, you're all set. A punch might be hit too hard or too wobbly to allow you to hit well on the next wrap.
Practice
In every sport, practice is essential. Tetherball is the easiest of all ball sports to practice all alone. Here are a few skills that can be improved greatly in solo practice:
- Hitting a ball every time it comes around.
- Power serving.
- Extreme angle serving, and receiving such serves. (Just receive your own serve.)
- Hitting sacrifice wraps, then moving forward and using the palm-fist combination to get a solid first offensive hit.
- Saving the ball at the last minute. Wrap the ball to within two or three wraps of the end, then jump up and block it from finishing. In game situations, the last few wraps can be the hardest for the player on offense to control, and this gives the defender one last chance to regain the ball.