[Note: this is #7 in a series of 20 tips to be published during 2009 & 2010.]
Your wheel is strong because the hub is centered inside the rim by opposing sets of spokes. Better wheels enjoy high tension in these opposing sets but the structure is less stable in case spokes are missing.
The low tension of everyday wheels is actually in their favor. With lower tension, the balance between spokes is not precarious. If one breaks, the wheel's trueness is only slightly disturbed and it runs nearly straight. Not so with high tension, lightweight wheels.
That's the reason you should only replace spokes one at a time. For example, if a chain overshift damages some of your drive side spokes, don't remove them all at once. Same is true for other forms of damage, like contact between a fellow rider's pedal and your unlucky wheel.
Replace broken spokes first. Insert each and tighten until its tone, when plucked like a guitar string, is similar to intact neighboring spokes (from the same side of the hub). Once broken spokes are replaced, change out any that are damaged (scratched, bent, deformed) but only ONE AT A TIME.
I'm no fan of de-tensioning prior to such a repair. Some guides recommend lowering tension in all spokes before undertaking replacements. It makes intuitive sense since a lower tension wheel is more stable, but it's simply not necessary and slows you down. An exception would be a super light, over tensioned wheel that's right on the limit. Removing a single spoke from such a structure might prove fatal and de-tensioning could be your only option. Such wheels are potentially dangerous and, hopefully, rare.
In all normal cases, just remove and replace spokes one at a time (tightening according to tone). Once all your replacements are done, spin the wheel and do some light truing. You'll find this strategy fast and effective.
If, when doing your final truing, you find it impossible to center the rim without unacceptable tension (too high or too low), then you've got a bent rim. Unless you straighten the bend, spokes are no help. Gentle levering can do the trick but experience pays. To gain experience, try straightening every wrecked wheel you can. Even when a rim is scheduled for replacement, take a stab at straightening, just for practice.
Some straightening techniques:
(1) Slip the bent section of rim into a narrow space (partly open drawer) and force the section one way or the other.
(2) Place the wheel on its side with the bad section between two wood blocks, bend facing up. Tap on the bend with a soft headed mallet or use another block and hammer. Easy does it.
(3) Lay the wheel on the ground before you with the bend facing down, centered between your feet. This is my favorite.
Feet put to use.
Place your feet to either side of the bend. The wheel touches the ground in two spots: the rim, midway between your feet, and the hub axle. Press down gently with your feet, which pushes the rim opposite of its bend. With practice, you can exert large forces with great precision and correct most lateral rim bends without the kinks that often accompany mallet or levering work.
I don't bother to loosen spokes prior to this adjustment. Just bend the rim back and make small truing corrections later. I hope you take my word that, with some practice, you can make 100% undetectable repairs to otherwise-fatal lateral rim bends in mere seconds.
It doesn't always work but it's always your best re-bending strategy. Honestly, I'd like you to be in the same position I've found myself: enjoying the applause (quite literally) of onlookers who can't believe I've fixed their wheel so fast, they think I'm a wizard. Nope, just a bike mechanic. You can do it, too!