Want to see what everyone is talking about with this whole 'Single speed revolution?' Before you commit several hundred dollars to a single speed bike, try it out on your current bike without costing you a dime. All you need are basic bike tools to get it done.

Step 1: Choosing a Bike

Since the aim of this project is cheapness, use a bike you have laying around. Many bikes will work for this, as long as it has one crucial component, a horizontal ( or horizontal-ish) dropout. While it is possible to convert a bike with any dropout to single speed, it takes either a great deal of time or money, neither of which are appropriate for testing the waters of single-speed bikes.

Other things to look for:
If the bike has horizontal dropouts, it will work, but if you have the choice, get a frame without brazed on cable stays. They will only affect how your bike looks, but appearance does count sometimes, and single speeds look cool, so why mess with it.

Step 2: Break the Chain

Use your chain tool of choice to break the chain.

try to avoid pushing the pin all the way out, it's just bad form, but in this case it doesn't really matter since you'll be loosing several links anyway.

Step 3: Take Off All the Stuff You Don't Need

Derailers, front and rear go
It helps if you remove the cable first, sounds obvious but don't forget.
Shifters go
any cable guide you can get off
All the cables also

Step 4: Admire the Nice Clean Lines of Your New Bike

Ain't it pretty without all those derailers in the way?

Step 5: Running the Chain

The main problem with this design is that you really have no choice of gear ratios. The chain line chooses it, and you have to take it. With a derailer-less bike a straight chain line is extremely important. If it bends too much, it will skip off while riding and leave you in a bit of a lurch.

Step 6: Attach the Wheel

screw on the wheel, but not to tightly, just finger tight is good enough for now. Try to have it as low in the dropout as you can.

Step 7: Establishing the Gearing

sight down the chainwheel to try figure out which sprocket best lines up with each chainwheel. Pick the gear ratio you are most comfortable to use. It's a bad picture, but hopefully you can get the idea.

Step 8: Tensioning the Chain

The chain will likely be too long. If so, adjust the chain tension by moving the rear wheel further back in the dropouts until the chain is nicely taught. The easiest test is it should run smoothly; if it's too long it will buzz, if its too short it will bind.

Step 9: Test Drive

Once the chain is in place, tighten up the axle bolts and take it for a spin. Take a wrench with you just in case the chain comes off and you need to readjust it.

Step 10: Clean Up

After all this mucking around with your chain your hands are likely covered in a layer of grease, making you unfit for human contact. This plagued my bicycle filled existence until I discovered the best degreaser, Laundry detergent. Just rub some on your filthy hands and watch the grease melt away. It's amazing.

Step 11: Verdict

I've had the setup for about a week, no way in hell am i going back to a derailer, at least for my urban bike (on a mountain, thats something different). Give it a few days before you stop having that impulse to switch into a higher gear when your spinning away, after that you really start to enjoy it.

Also, depending on the gear ratio, give it at least a few days to adapt, at least until your not crying 'rape' from spinning so fast after every ride.

Step 12: Observation

It's been a while since I turned my bike into a single speed by this less than secret method, but since I did it, I seem to have noticed a fair number of other single speeds pop up. Most of them follow the same methodology, just removing unused parts. Fair enough, I encourage it, but a fair number decide to do away with one of the brakes. Now it is true that the front brake does generate most of the stopping power, that is still no reason to remove the rear, and its a great reason not to only ride with a rear brake. By limiting yourself to only one brake you greatly reduce the versatility of your bicycle. While you may be fine most of the time with only your front, there will come a day, maybe on a long downhill, maybe a wet road, or maybe a cable snap that you will wish you had another method of slowing down. But if you're really willing to castrate your bicycle in such a manor, be my guest, just try not to crash into me.
By the way, the above only applies to freewheel bicycles, and seemingly only so single speeds. I have yet to see a person with a derailer equipped bike decide one brake is enough. If you ride a fixed gear, the fixed gear is a rear brake, and is more than enough stopping power most of the time. It's not a bad idea to ride with a front brake though, just for when the inevitable happens and your chain snaps, or something like that.