This kind of project isn't one that should be fiddled with at all if you don't know what you are doing. Too many ways for things to go bad (fire, death, loss of computer equipment, etc.)
But richms has the right idea. You would need to find a relay that uses a small enough current to activate it (no more than a couple hundred ma), so solid state is best. And the capacity needs to be rated high enough to carry the power required by your monitor. Then, of course, you need appropriately sized wire and a circuit board to tie it all together. You might be able to do it without a PCB, but that's not really safe nor recommended.
But seriously, if you can't picture how this one goes together in your head, you should find another method.
RandyT