There isn't really a big trick. The main thing is you will want the aperture as open as you can get it without hitting depth of field issues. You are likely to have a lot of trouble accomplishing your goal with a P510 as well since the low light quality seems to be spotty at best. Most of the photos you linked were probably shot on fairly high end gear with really solid low light capability (noise free out to the high 4 digit ISOs where as the P510 doesn't make it to 4 digits without noise issues.)
On stage there should be enough light, but it'll probably be tricky to get the balance of light on the subject and the light effects that you want without issues. It can be fairly tricky even with high end gear. Your best bet will probably be to experiment and play with the exposure compensation. Also, if you can, don't be afraid to use the flash to fill in faces while still getting the lights in the background if you have problems with dark faces while trying to get the lights.
Update: I'd defer to KeithS' advice since he has the camera and I'm only able to work from reviews about it. It may also very a lot based on how much light they actually have on stage. (Some stages are actually very bright, where as others are not, it really depends on how they do lighting.) Do expect to need to do a lot of color work in post though, stage lighting is always tricky since it is filtered light of a variety of different colors or in some more modern cases, single frequencies of light coming from LED Parcans.