A modern (Korean War era and later, at least) signal mirror has a hole in the center, and the hole is surrounded by a grid of retroreflectors. You aim the mirror spot at something close by, then look through the hole. The grid makes a very bright spot where the mirror's reflection is going. You then simply tilt and rotate the mirror to put that spot on your target.
This is a good photo of what it looks like.
As the comment in the image says, that hot spot is not the sun itself. It's showing you where the reflected light from the mirror is going. Just put that spot on your target and there you are.
Note that if sun-to-mirror-to-target bounce makes a fairly shallow angle, say more than about 135 degrees, the retroreflecting grid doesn't work and you have to use the methods given in other answers here. Which are also, of course, useful if you don't have a real signal mirror. So the other good answers in this thread should not be ignored.
Image ganked from this flickr page. As it says there, several companies do make "signal mirrors" that appear to have a grid around the hole, but don't actually have retroreflectors and don't make the bright spot. (I can confirm this; I bought one and was disappointed.) If you buy a US signal mirror on eBay and it says "Mark III", it's the right thing.