You've already said you hear a click when you turn the key. That click is the solenoid engaging.
Under normal operation, a motor will have a near-zero resistance--hence the large current demand when starting your car. However, when a motor fails, it will function like an open circuit/near-infinite resistance. When this is the case, instead of measuring a VD of zero across the starter's terminals you will see the entire battery voltage. To find out if this is the case, bump the starter with the headlights on. If the headlights don't dim at all, then you've got a bad starter. If they dim, it would be worth your while to have the battery/charging system checked before doing anything with the starter.
If the starter is bad, I would strongly recommend buying a new one--I was able to have an ACDelco starter installed in mine last summer for under $100, and that includes a warranty that is good at any ACDelco service center.
If your car is a stick, keep in mind that you can start the car by popping the clutch--just don't do it any more than you absolutely have to, and make sure you have the ignition on when you do.
If this isn't clear enough, let me know. I worked for an automotive shop in high school that specialized in electrical repairs, and I'm currently a junior working on an EE degree--I'll be glad to help as much as I can.
Dave