Spokes radiate from the hub to the rim, where they are anchored in a screw-thread attachment called a nipple. The nipple has flat faces which may be turned using a tool called a spoke key (available for a small cost from any good bicycle shop, in extremis a pair of pliers will suffice); thus the tension in an individual spoke can be increased or reduced.
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 relevant to the process of truing.
Put simply, if you tighten the spokes coming from the left side of the hub, the rim will be pulled to the left. So if a wheel is "out of true" - deflected - to the right, tighten the left-side spokes near the deflection and loosen the right-side spokes.
It is important to maintain the wheel's tension correctly, so if you tighten a left-side spoke, loosen the right-side one. All the spokes on one side of a wheel should be at approximately the same tension; a quick test is to "ping" the spokes with a fingernail: they should all sound the same.
To avoid putting undue torsion (twisting force) on a spoke, it is good practise to go slightly over and then wind it back. So if you were adding a half-turn to a spoke, you would go to three-quarters of a turn and then come back a quarter turn.
Bicycles with asymmetric rear wheels have shorter spokes on the drive side - the side with the cluster of sprockets - under more tension than the spokes on the non-drive side. Whatever the look of the wheel, it is correctly true when the rim is exactly on a centreline drawn between the wheelnuts (the exception to this is bicycles with offset rear triangles, an exotic touring variation; you'll know if you have one).
A full, comprehensive discussion of bicycle wheel building and truing is found in Jobst Brand's book The Bicycle Wheel.
Note: This discussion of truing applies to conventionally-spoked wheels, and may not be relevant for the new road-racing style of wheel with very few spokes.
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