link I have actually done this and I have the definitive answer! :) I learned to ride a bike by myself when I was about 22.
1. Buy a bike. This will be hard because you won't be able to help the bike salesman fit you. I got a Gary Fisher Tiburon hybrid bike for about $250.
2. Remove the pedals with a wrench. The result will be an absolutely pedal-less bike.
3. Lower the seat as low as it will go.
4. Find a slightly graded field--not a steep hill. Practice 'running' the bike, and then lifting your feet up and balancing. Do this a lot. Eventually you will become totally comfortable keeping the bike balanced and it will be awesome.
5. Reattach the pedals. Stand straddling the bike (as though were 'running' it). Engage the brakes, and put your left foot on the left pedal and your right foot on the ground. Rotate the left pedal so that it is at the top of the downstroke (about 2 o'clock, looking at the bike from the left side). Then disengage the brakes; your weight will create the downstroke, and you can easily start pedaling. Off you go!
I taught myself to ride a bike this way a couple of years ago and have been happily riding since. The key is to remove the pedals. This makes learning a lot easier. Also, knowing how to get on the bike and start it going is a big help.
Other advice:
1. Steer by leaning, not by turning the handlebars.
2. Practice braking. Get going really fast, then stop on short notice. One of your brakes will be for your front wheel, one for your back wheel; use them both, but especially do not brake with only the front wheel. You need to learn how to brake because otherwise you will get into accidents because you don't squeeze the brakes hard enough.
3. Check out the articles by Sheldon Brown. They are a great help if you're teaching yourself to bike.
That's it! Good luck! You really can do it, it's great fun. Just for clarification, I learned how to ride by myself on a nice grassy field, which I highly recommend. After that find a big wide bike path. It took me a couple days of serious time commitment to get my balance in gear, so it won't happen in just one day. Also, you will almost definitely fall off and hurt yourself--wear a helmet and gloves.
For what it's worth, teaching yourself to ride a bike is fantastic and just like you'd imagine it; you fall, you get up, you fall, you get up, etc. It's like Beckett said: Try; fail; try again; fail again; try agian; fail better.