A bicycle wheel consists of a central hub and a round rim, joined by a number of spokes. Spokes radiate from the hub to the rim, where they are anchored in a screw-thread attachment called a nipple. By tightening and loosening the nipples, it is possible to bring the wheel back into round (vertical true) or remove a side to side wobble (lateral true).
Spokes may be arranged in a variety of patterns, of which three-cross, four-cross and radial are the most common. The pattern affects the strength, weight and characteristics of the wheel but is not particularly relevant to the process of truing.
To build or to maintain a spoked wheel, a spoke wrench is necessary. The flat-to-flat dimensions of a typical spoke nipple are too small to fit any commonly-available open-end wrench. Any good bicycle shop will, however, stock a selection of spoke wrenches, with price and quality being proportional.
A spoke 'twiddler', or nipple driver, is a tool that may be useful in the course of assembling a new wheel from its component parts - hub, spokes, and rim. It isn't necessary - especially if you aren't building a wheel - but it can save some time. Similar to a screwdriver, but with an off-set blade that rotates freely in the handle, it is used on the slotted outer face of the nipple - which resembles a slotted screw. A spoke 'twiddler' allows for rapid assembly of the wheel - or installation of a nipple on a single spoke - and is designed to self-limit the extent to which a nipple can be threaded onto a spoke.
A spoke wrench is used to bring tension to the spokes, and is applied to the square part of the nipple that protrudes inward at the rim. Unlike the 'twiddler', the spoke wrench is designed to turn the nipple when the spoke is under tension. This difference is what makes the spoke wrench essential.
A truing stand is a purpose-built stand into which a wheel (rim, spokes, and hub, with axle) is installed during wheel-building, wheel repair, or wheel maintenance. A truing stand is very useful - possibly essential - for making hand-built wheels. Effectively, it is a rugged, precision-made jig for holding the axle of the wheel solidly in place. By extension, the rim thus has a steady reference in the axle in the hub held in the truing stand. The rim is, therefore, also found in relation to a caliper, or set of calipers, built into the truing stand, and against which checks are made for radial and lateral true (read 'perfection') during the course of building or adjusting a wheel. For extreme accuracy in measuring true, an optional dial indicator may be fitted to the truing stand, and a separate tensiometer may be kept to hand to test for proper tension on all the spokes (tension-balancing). Instructions for creating an inexpensive, but very accurate, truing stand are here.
A dishing tool is used to measure the extent to which the axle juts out past the rim. Since a true wheel has the plane of the rim centered laterally between the points on the axle at which the axle is fixed to the frame, the offset of the rim from that anchor point on one side of the wheel should be identical to the corresponding offset on the other side. A dishing tool is used as a comparator: the offset on one side is measured using the tool, that setting is 'stored' in the tool, and the tool is applied to the other side of the wheel for purposes of comparison; the deviation of the second side's offset from that of the first's indicates the direction in which, and the extent to which, the rim needs to be moved to make the wheel true. However, a dishing tool is not strictly necessary if you have a good truing stand: if it's understood that a true wheel (abstracting from the particularities of the hub and the spokes) is symmetrical (i.e. the rim itself is, in some sense, 'centered' on the axle) then you can use the truing stand's caliper (or calipers). and an occasional flipping of the wheel in the stand, to serve the same function as a dishing tool.
In most cases, especially when truing as maintenance on a wheel that has already been built, checking the tension on the spokes by ensuring that they all make the same tone when "pinged" with a fingernail will work fine. Checking the dish is also unnecessary on minor repairs, as most good truing stands will be able to give an accurate idea of how close the wheel is to centered, though it is probably a good idea to take the wheel out and re-settle it in the stand to double check. It's necessary to measure the distance if you are truing a wheel that is meant to have an offset, but this is very rare.
In a situation where a stand is not available, the brake calipers on a bicycle can be used to measure true while the wheel is still attached, but this is less than ideal. Also, if no other option is available, a small adjustable wrench can be used instead of a spoke wrench or key, but extra care should be taken not to strip the nipples. A glass cutter made by Richards has one opening small enough that it can be enlarged slightly to make a passable 0 spoke wrench - or a 1 or 2, if that's what you need.
If a rim has been 'pringled', or 'potato-chipped', into a saddle shape, by a lateral blow, it will be difficult to straighten by spoke tensioning alone - in fact, it is probably impossible to overcome severe rim warping this way. Often, however, it is possible to restore the wheel to a nearly-true state, even if it seems hopelessly warped. The procedure that follows should be applied as soon as possible after the trauma; leaving the wheel in it warped state for more than a few days will likely cause the wheel to cold-set - meaning it will retain the new shape in which it is left, and probably will have to be replaced.
In order to effect the following quickie repair, you must have a properly inflated tube and tire still on the rim, and the rim itself should only be generally out of shape, with no damage to the rim wall itself. To wit: standing with your feet shoulder-width apart, with both hands, grip the wheel firmly by the rim and rubber at the point directly opposite the point on the circumference that is most obviously bent away from the principle plane of the wheel; bend slightly at the waist and position the point of the tire opposite on the ground in front of you, with the wheel at an angle of 45 degrees to the ground (possibly greater, depending on the denomination of the tire), and the bent part heading earthward; raise that point off the ground a few inches and let it fall again, ensuring that in the next step, only the tire - and no part of the rim - is going to strike the ground; without straightening at the waist, or bending over further, raise the wheel off the ground to about head or chest height, then forcibly bring the wheel down in such a way as to strike the ground sharply with the inflated tube and tire at the point opposite your grip; the rim should pop back to very nearly true. You can't undo damage done by striking the rim on the ground, so plan carefully, and rehearse mentally before committing to this repair.
If the quickie fix above has improved matters, it's usually possible to improve the situation further with the usual techniques required of truing or maintaining a wheel.
In the event that the above procedure doesn't bring the rim back to at least a rideable state, it may be necessary to replace the rim or the entire wheel. Note, though, that a rim can often be straightened, at least to some extent, by placing the rim (with appropriately loosened spokes) between two rigid objects (e.g. a pair of closely-spaced pipes, or between a door and its cross-wise bar-like handle) and, using a prying action, creeping up on the desired degree of 'flat'. Don't bend the rim more than necessary, work iteratively, check frequently on your progress, and be aware that you may need to overshoot your target slightly to allow for the tendency of metals to spring back from bending.
It should be noted that repairing local rim damage with pliers or even a hammer and anvil is never advised - because less dramatic, more effective, methods are available which will not cause even superficial damage to the rim wall - the all-important braking surface in most cases. Instead of pliers neat, repair a flairing of the rim by sandwiching the rim between two thin, very flat pieces of metal (e.g. two cone wrenches) and placing this in the jaws of channel-lock pliers. An alternative method for repairing rim flairing is to use blocks of wood as both anvil - below the rim - and hammer - above the rim. If it seems necessary to use a hammer, don't strike the rim directly with the hammer's face; lay a strip of aluminum or brass over the area of the rim to be repaired, and strike there. Aluminum cans - ubiquitous and easily cut with scissors or even a pocket knife - are indispensable in bicycle repair.
Truing the WheelEdit
First, remove the wheel from the bike and remove the tire and tube before placing it in the truing stand. Adjust the arm and caliper on the stand so that the caliper is just shy of touching both sides of the wheel. Now, spin the wheel and slowly close the stand's calipers until they scrape against a spot on the wheel.
Once you've found a spot where you are out of lateral true, tighten the spoke or spokes on the side opposite the bump, and loosen the ones that are pulling it out of true. Be patient while doing this - you shouldn't be going more than a quarter turn at a time while truing like this. If the spokes are giving resistance, try over turning slightly, and turning back to where you intended.
After you've gone through several passes like this, you should check the vertical true of the wheel to make sure that you haven't put it out of round. Re-adjust the arm and caliper of the stand so that the calipers are together and just underneath the rim. Spin the wheel, and this time adjust the arm until the wheel begins to scrape.
While adjusting for vertical true, you should tighten the spoke at the center of the hump, and tighten the spokes to the sides one half as much each. Because these spokes will be on opposite sides of the wheel, this will ensure that you don't put the wheel very much out of lateral true. If the hump is between two spokes, tighten them equally. Adjusting the spokes in one place will affect another section of the wheel, somewhat like squeezing a balloon.
After this is done, you should check for lateral true and even tension, retruing for both lateral and vertical true if the wheel is out.
If the wheel is properly trued and tensioned, you should stress test the wheel by placing it on one side and pressing down on it fairly firmly. You should repeat this going around the wheel, in order to be sure that the spokes settle into position with the spokes that they cross now and not while the wheel is being ridden. This can also put the wheel out of true again, and this should be checked.
A full, comprehensive discussion of bicycle wheel building and truing is found in Jobst Brandt's book The Bicycle Wheel (ISBN 0960723668).
-  - Sheldon Brown's page on bicycle wheels, wheel building and truing