Bicycle wheels need to be properly adjusted for smooth riding and to prevent the rim from rubbing against the brake pads. The most common cause for misadjusted wheels are accidents and lack of maintenance. A rim with a dent or other damage is practically impossible to realign; any attempt to do so by pulling it back into shape will cause broken spokes, or spokes that continuously unscrew and go slack. Replacing a rim is much easier than building a wheel from scratch.
Buy a new rim with the same number of holes and the same inner diameter. The inner diameter is smaller for some "aero" rims. Avoid black-anodized rims because the anodizing will rub off after a while. Always use aluminum rims, never use steel. Steel is hard to true and brakes poorly even with special brake pads.
Place the old wheel flat on a table and tape the new rim to the old one, making sure that the valve holes line up. Also make sure that the spoke hole pattern lines up if the holes are alternatingly offset left and right from the center. Next, loosen all old nipples but do not completely unscrew any of them. Beginning with the spokes ending at the flange facing up, unscrew the nipple and move the spoke to the new rim, one at a time. A few turns of the nipple suffice. Apply a small amount of grease to the threads before screwing on the nipple. Continue with the remaining spokes until none are attached to the old rim, which you can now remove. The wheel will be very floppy at this stage. To avoid losing nipples in the rim, screw the wrong side one turn into a spare spoke, which you can then use as a handle.
If the old rim was built with the correct spoke lengths (which are different on the left and right side for the rear wheel), the threading of the spokes was completely covered by the nipples. Now carefully tighten all the nipples until the threading is just barely hidden. This must be done carefully because it ensures lateral trueness. All spokes will still be rather loose after this. I use a power screwdriver. Next, beginning at the valve, tighten every nipple with a spoke wrench by one half-turn, in sequence, until you reach the valve hole again. Repeat until all spokes feel about as tight as they were in the original wheel. For rear wheels, tighten the spokes on the sprocket side much more than the ones on the outer side to keep the rim in the center. This sort of happens automatically with the above method because the sprocket-side spokes are shorter than the outer ones, but it helps to complete the sprocket side before beginning with the outer side. Get a feel for the spoke tension before taking apart the old wheel.
The wheel is now tight but not true. Install it on the bicycle and turn the wheel to see where it rubs against a brake pad. If it does not turn at all or rubs in too many places, loosen the brake cable so that the brake pads move away from the rim. In places where the brake pads rub, tighten the opposite spoke until it no longer rubs. Always tighten neighboring spokes too. Never tighten a nipple by more than a quarter-turn at a time before rechecking. If a spoke seems to become much tighter than its neighbors, loosen the spokes on the opposite side (i.e. ending at the hub flange on the rubbing side) instead of further tightening. When the rim no longer rubs against the brake pads, move the brake pads closer together and repeat, until there is about one millimeter between the pads and the rim on either side, on average.
During trueing, periodically pull every pair of neighboring spokes on one side together as hard as possible with one hand. This releases tension that builds up in the spokes during trueing because tightening nipples also twists the spoke. It may help to pluck spokes and comparing the pitch of the sound, but I find this method hard to use and inaccurate.
After the wheel is finished, reinstall the rim tape, the tire, and the tube, inflate, and ride around the block a few times, then recheck the wheel by releasing tension again and checking trueness. Traditionally, tires are mounted such that the label is at the valve on the right (chain) side of the bicycle.
Check out the site of DT Swiss, the largest maker of bicycle spokes. Their glossary is very good.
See also technical articles on "Steering"
