They way I do it is I proved the Arduino with power using a 12V supply through the power jack. Then on the Video Experimenter board I pull out that 12V from the Vin pin and feed it into my camera.
The camera it’s self should have 3-4 wires. It will have a signal, power, and probably two ground wires (one for the signal ground and one for power ground). In my case the camera came with a nice little connection that packs the wires into RCA and power connections nicely for me. So then the RCA wires go into the Video input side (red RCA in my picture), and the power connects into the Vin(yellow wire in my pic) and ground(black wire in my pic).
As Michael said, RCA is for signal, not power… Do not try and supply your camera with power through its RCA connection. This will very likely destroy the camera.