So, the quick answer is to take inventory of what is wrong with the bike, and start by fixing the things that seem possible. I'd be inclined to start with the absolute basics:
- Make sure the brakes work.
- The tires hold air, and
- That you've got at least one gear that works.
Just take it slow and fix things one at a time, aiming for a bike that you're not afraid to ride in an empty parking lot, then for one that shifts, and so on…
I'd probably go to the library to get a good book on bicycle maintenance, maybe one of Zinn's books, but you could Google, or ask here – whatever feels like the right way to get the information you need. If you're in a city of any size check to see if there is a bicycle co-op where you can take the bike to hang out and work on it. You're real likely to have fun, get some good advice, and learn your way around the world of bicycle tools.
For an old bike that's been flooded you should probably think about:
- Replacing brake and shift cables and housings.
- Cleaning, lubricating, and adjusting the headset, bottom bracket, pedals, and wheel bearings.
- Lubricating and maybe replacing the chain.
- Adding a bit of penetrating oil to all of the spokes so that they're likely to move when you want to adjust them.
- You may need to replace the free hub body (or soak it in a good penetrating lubricant like Kroil).
If you keep in mind that this is a learning project and something that is supposed to be fun, you can putter away at fixing things and understanding how to work on a bike. Undoubtably you'll find things that you "should" spend money on – but that doesn't mean you have to. If the bearing races in your hub are shot, you could get a new wheel, or you could replace the balls, add plenty of grease, and adjust them as best you can. It will work for a while, maybe a long while and you'll have learned something and saved some money. In the meantime keep an eye on craigslist for a deal on a wheelset.
If you approach it as a learning experience with a budget, I think you can easily get by for $300.