The short explanation is: Set a long shutter speed.
How long depends on what sort of motion you're shooting. Really fast things won't need a very long shutter, slower things will need a longer shutter. Basically you want the shutter to stay open long enough to capture the subject in more than one position, creating the blur. Different situations will call for different settings.
Of course, the shutter speed affects the entire picture, so the singer you mentioned would have to stay a lot more still than the band to come out sharp. If the singer moves then he/she'll come out blurry too.
The easiest way to pull this off with your camera would be to put it in shutter priority mode ("S" on the mode dial). This allows you to pick a particular shutter speed and the camera will adjust the other settings automatically. Try something around 1 sec and adjust it from there. (However, that will probably only work in dark places. Anywhere else the light will be too bright to allow a 1 sec exposure.)
(I'm doing my best to answer ALL your questions, SeanC...

Let me know if I miss one.)