Relay with external power?

Sorry for the late response, had to get through finals before I could come back to thinking about this. Okay, so I'm going to try to follow SirNickity's response and expand my horizons. Google is not providing me with much luck, so if someone could point me in the right direction, that would be much appreciated. I need to build something that will run off the Arduino's I/O ports with at least 10 separate channels. To restate OP, I'm trying to make a portable, music-synced light show.

I must admit, this feels awfully over my head...