It really depends on the games.
Some use vector monitors (Omega Race, Asteriods, etc.), you'd need a special interface for these to hook to up to a PC, and a modified version of mame to control it.
Some use a monitor with composite video input(Pong clones, maybe Space Invaders), you could just hook it up to a video card's TV-out (you can get an adapter if your card only has S-Video).
A few even use a B&W TV set to channel 3 or 4 (mostly Pong clones). You'll need to hook up a VCR to it and the TV out of a video card to the VCR.