Digital cameras in general are hard to use for sports action because there's a pretty long lag between when you press the shutter button and it takes the photo, so the most important thing is to practice your timing... anticipate the shot and press the button about 1/2 second before the "moment." In tennis, i'd say you're going to want to click as early as when the ball leaves her opponent's raquet or before the ball goes over the net, (if you want a photo of her hitting it back) but experiment.
Hopefully the court is very well lit, because you'll want to use a fast shutter speed. I'd say go into Tv mode, and set the shutter speed for at least 1/125 (or faster if there's enough light) If it's too dim to shoot 1/125 at ISO 50, try ISO 100 or 200 (400 is super-noisy, try to avoid it.)
auto focus slows down the camera even more and is useless on a moving target, so use manual focus. the fastest way to do that is autofocus on her when she's standing still, then press "MF" and that will lock the focus as long as she's in the same place, then re-focus whenever she or you changes position.
same with metering: the big lights will mess up your metering, so use spot metering on her (probably best to set it to her white outfit and then lock it)
and those lights might be tricky for auto white balance, so set that manually, too.
Then just try to get a lot of shots and a lot of variety of shots. Vary your position, zoom, camera angle, height, distance, and composition in the hopes that something works. Don't just take 200 shots from the same place.
Hope that helps. If you can get a tripod before the match, that will help a lot, even if it turns out the light isn't good enough to use a fast shutter speed and you can't get a good shot of her without some motion blur, at least the background will be sharp and it might look arty enough to use.
Good sports photos are really tough as it is, and the limitations of a digital camera make it even harder, so just shoot as much as you can and hope for the best.
One last thing, even if she begged you to come take photos, try not to distract her, you don't want to get blamed for a loss. I'd say turning off the flash would be a good idea, unless you're practically on the court, it's not going to make a difference anyway.
Bryan