Some people use a "Smart Strip" for this, but there are reports of this causing damage to the monitor.
A relay is a possible solution. Just grab a suitably rated relay and wire it in-line with the AC power for your monitor. I'd suggest switching both sides using a dual pole relay. I'd suggest a 10A contact rating minimum, and go for a 15-30A if you can find one. The inrush current on a monitor can be pretty high, and overspecing never hurts.
12V relays of this nature are more common than 5/6V, and they are readily available at e.g. Radio Shack or from online suppliers like Digi-Key, Mouser, Jameco, etc. Just run the coil off the appropriate output of your PC supply, and things will turn on whenever the PC is on.
Remember that you're talking about a home-grown AC power solution. Always keep safety in mind. You don't want to shock yourself or start a fire.
My solution when I have a PC in an arcade cabinet is to just wire the AC line for the PC off the cabinet AC distribution block which is switched by the cabinet power switch(es). Set the PC to automatically start upon power return. Proper shutdown (if you desire and/or is required by your setup) is still possible: just hit shutdown, wait for shutdown to complete, then power off the cabinet.