Yours is a common story. This is pretty much what you need to do:
1. Replace the tires and tubes. Rotted rubber can cause a serious accident. Don't fool with this.
2. Replace the brake and shifter cables. You can get the cables and housings pretty cheap if you look around.
3. New chain. Trying to salvage a rusted chain is a waste of time.
4. Attack the chainrings and cassette cogs with a good rust remover (Naval jelly, coke, or whatever) and a wire bristle brush. Cassette innards can survive a lot of neglect. If it's toast, get a new one for $25-30.
5. Headset, bottom bracket, and hub bearings all need to be checked and serviced as necessary.
6. New brake pads. The old ones are usually rotted and junk.
7. Remove (if you can) and grease the seat post.
That's pretty much the minimum. If you need specifics on how to do the individual tasks, visit:
http://www.parktool.com/repair/byregion.asp
Almost all the overhaul proceedures you need can be found there.
Good luck!!!
P.S. Get some PB Blaster. You're going to need it ;-)