Indoor action shots with no flash?

I have a nikon d60. I was at my sisters divemeet which was indoors and i had no idea what to do on my camera. I want it to be a goid picture and not look ahaky. Is this possible? If so how do you do it?

When shooting indoors without flash, you have only two solutions.
1. Raise your ISO. That will give you usable shutterspeeds in many situations, but the digital noise can be a major problem. The normal kit lenses (18-55mm and/or 55-200mm) aren't "fast enough".

2. Get a faster lens. If you get an f/2.8 or faster lens, you'll be good to go. I shoot NCAA and NBA basketball, and using flash is forbidden. The only way to capture the action, and not have photos that are blurry or digitally noisy was to get some faster optics. I use a 70-200mm f/2.8 for my long shots, and a 50mm f/1.8 or 35mm f/1.8 for my closer shots (I usually shoot directly under the basket).

Remember, your D60 requires AF-S (for Nikon) or HSM (for Sigma) lenses for full auto-focus compatibility.

Without a flash, don't expect to capture a sharp image of her flying through the air. With a tripod and telephoto lens you might capture a good shot of her on the diving board just as she is getting poised to go into her dive. Take some trial shots of the board and of people whose dive you don't really care about, so that everything is nicely dialed in by the time your sister is where you want her for the shot you want.
Assuming the lighting will be consistent it could be best to use manual exposure. That way you can perfect the exposure with your practice shots, without the metering getting confused by a diver's different position or bathing suit.

It could be good to use a lens hood. You never know if a spotlight is going to be in a spot that would otherwise cause lens flare.