This method is for the homegrown type who don't have or want to shell out $100-$300 for a fancy new wheel set, and don't mind a rough-around-the-edges look. I would not recommend taking this step if your bike is valuable or you think you might be selling it any time soon.
Also for any cyclists who want to learn how to unbuild and rebuild a wheel, this instructable will take you there, just skip the masking and painting steps.
I used a rear wheel, 27" 36 spoke, 3 cross setup for my demonstration, but most steps will be the same for other sizes or spoke numbers and configurations. If you are using a front wheel, it will be easier because you won't have to worry about different spoke lengths and dishing.
Hope you have fun and learn something here!
Step 1: Wheel Disassembly
1.) [Deflate tire first, then] Remove tire and tube--using a tire lever or screwdriver (use caution so as not to rip/puncture the tube), pry the tire off on one side of the wheel, then work your way around. You will probably need to use to levers and work against each other. Once the wheel is half off, peel the tube out from inside it, using care when removing the valve stem from its hole. Then the other side of the wheel should come off relatively easy
2.) Take spoke nipples off--Using a spoke wrench or screwdriver, start by loosening the tension on all the spokes evenly, to avoid "potato-chipping" the wheel (i.e. uneven high pressure spokes distort the shape of the wheel into a non-round shape). Then keep going around and remove all the nipples from the spokes and collect the nipples and spokes in a place where they will not get lost/damaged/dirty. If you are working with a rear wheel, make sure you keep the inside and outside sets of spokes separate, as they should be different lengths.
You should now have an empty rim, all your spoke nipples, your spokes, and an empty hub, and this is the perfect time to give them all a good cleanup, especially to prevent nipple-spoke seizing.