The string method works well, or use a real compass if you have one (it's a drafting tool).
I cut the holes using a medium tooth blade on a sabre saw, but the best method is to use a circle jig and a plunge router with a 1/4-inch straight bit. Some routers come with the jig, or you can get them at woodworking stores.
Depends on how handy you are, what tools you have, and how professional you want the result to be. In a pinch you could even cut the holes with a small, pointed hand saw called a "keyhole" saw... they're cheap. But be prepared for nasty tear-out.