I would like to achieve this effect using my Nikon P510:
Are there any suggestions or tips that would help me do that?
Based on how the second photo looks, my guess is that it was extremely dark and that they took a flash photo with a bulb exposure and then tilted the camera upwards to create the trails from the only lights in the room (which would have been the audio gear).
This would leave the DJ well developed since he is only exposed during the flash and then expose the light trail from the gear over the top of the initial exposure.
Could you be talking about the lines of light, they are commonly called light trails. You can get that effect using a torch. This page has a nice looking example in medium sized room.
The basic way to get that is with a tripod and a long exposure. This post has some more tips on it.
Depending how long the exposure is you will either see a dj with motion blur or they will be totally hidden, that will also depend on how much they are moving.
Edit: John Cavan's comment made me realize that my example above is slightly misleading. It's better described with the more specific term light painting.