How to get NO BLUR for no-flash pictures with a DSLR (specifically a Nikon D3000)?

I just got a new camera, the Nikon D3000, and I'm taking pictures of live bands this weekend. I did some this weekend, and I noticed a lot of them came out blurry because I didn't want to use flash. Is there any setting I can put it on to get the fasted shutter speed possible? Or does anybody have any advice?

Higher shutter speed.

A tripod could help if it is allowed. Of course that only steadies your camera, not your subject. With or without a tripod, you do want to capture a moment when at least their faces aren't moving much. (Motion blurred limbs are okay and can give the picture an interesting look.)
Turning up the ISO and opening the aperture can get you a faster shutter speed. Although the D3000 will have far less noise than a compact camera, by ISO 1600 noise is getting noticeable, and by 3200 it is getting very noticeable. Turning on the VR can help compensate for a little bit of camera shake, although it won't do miracles. If the lighting isn't being changed much, it could be best to use manual exposure mode. That way, if you have found an exposure that seems to be right it isn't getting upset by small changes in camera position that capture more dark background. Do experiments taking shots that may not be the most interesting moments, but allow you to dial in a good setting to be ready for the more photogenic moments.

You need to use faster lens (f/2.8 or less) with fast shutter speed (1/200 atleast) with an appropriately high iso (depending on your aperture 800-3200)