I've cleaned my keyboard recently and it still works 2 days later so I'd vouch for this method (becasue I don't have a dishwasher), but YMMV. This is the second-best method I know of.

For this method, you need:
1. A dirty, grimy computer keyboard (you read that right, this doesn't work for laptop keyboards)
2. 4-6 hours of free time (actually, you just need 1 - you'll have to wait for the next 5 though)
3. A toothbrush (preferably one you're not going to use for anything else, especially if you've spilt some really nasty stuff on your keyboard)
4. A tub long enough to accomodate your keyboard, and enough water to fill it to a height of 5-10 centimetres
5. A dust-free place where nothing will pass by and knock your keyboard off its perch while it's drying
6. A screwdriver. Cross-pattern (or whatever the official term for it is), preferably.
7. An expired/void warranty (otherwise you're better off asking them to fix/clean up/replace your keyboard). You have been warned - the following steps may render your warranty void if it isn't already so.
8. Enough money for a new keyboard (this is Plan B)

1. Unplug your keyboard. I cannot emphasise this enough.
2. Flip it upside-down. You see some greyish circles with crosses in their middle? Those are called screws (not to be mistaken for one-night stands). Remove those with the screwdriver. If you need help call a neighbour or your mum over.
3. Open up your keyboard very carefully. If yours is anything like mine, the casing should be comprised of 2 halves loosely fitted together, this shouldn't be too hard to open.
4. Once it is open, you'll notice it is made up of 5 main parts:

a) Bottom tray, containing a microchip and the wire that leads to your CPU.
b) 2 plastic sheets that overlap and look like they have circuitry printed on them (actually, they do - don't wet these or let anything come into contact with them!)
c) A rubber mat with little springy knobs corresponding to the positions of the keys on your keyboard. Don't damage this. You may clean this if it is dirty. Exercise extreme caution though - you don't want to damage the springy mechanism.
d) The top cover, and the keys associated with it.

5. Put parts (a) to (c) aside, on something clean, and cover them with something so dust does not collect on them (dust + electronics = nono)
6. Pop the keys out of the top cover (carefully). The quick launch buttons may be a little tricky, so be extra careful with them. This part may be a little tricky for the multimedia keyboard keys.

WAIT! Before you do so, ensure that:
a) You have another keyboard somewhere in your house, one that you have access to.
b) You have a diagram of a keyboard and its key layout.
c) You have memorised the key layout of the keyboard.

7. Good. Now fill the tub with water to a depth of about 5-10cm (2-4in). dump all the keys in. Now dump the top cover in. Use your fingers and rub as much crud off the cover as you can.
8. Use the toothbrush to go into the little nooks and crannies. The tougher ones may need (non-excessive) scraping. Use a toothpick for the hard-to-reach corners (like some of the F1-F12 keys).
9. When you're done with the tray put it aside. Now check through each key. Rub stains off with your finger. If that doesn't work you might want to try it with a little detergent.
10. There might be C-shaped wires attached to the Return and Space Bar keys. Remove these carefully prior to washing. Clean these with a damp cloth, and dry with a dry cloth. They might rust - that's a risk you have to take.
11. Once everything is clean, bring it somewhere dry and hot (the balcony perhaps; this could be problematic if you live in a cave like Osama). Give each key a good fling-dry, wipe the external surface (the part you touch when you type) clean, and lay it upside-down to dry. Do this for all the keys.
12. Don't stick the C-shaped wires back yet. Now do likewise with the top cover. If you're impatient use a hairdryer or a fan.
12. Grab a beer, and get in front of the television for the next 5 hours. Or create a new w/u on how to spend 5 hours doing nothing.
13. When everything is dry, carefully plug the keys back in the cover. You might find the tips below useful when doing this.

a) The directional keys are tricky. The up and down keys are displaced slightly to the left. the backstroke key looks a little like the left key, so it might help if you mark them with a sticky label or non-permanent marker after cleaning.
b) The keys have a trapezoid cross-section. The side facing away from you (on the keyboard) is usually steeper, while the side facing you has a gentler gradient.
c) Don't forget to stick the C-shaped wires back into the Return and Space Bar key, if they were there originally. Align them carefully before you plug the key back into its hole; test the key afterwards to double-check.

14. Now re-assemble the keyboard. Bottom tray at the bottom, followed by the 2 plastic sheets, then the rubber mat, then the top cover. Align them properly, there are little holes in the plastic sheets and rubber mat to help you with this.

a) Most keyboards have keyboard props on the left and right side. If these fell out during disassembly, replace them.
b) There is usually a guide rail for the wire that leads back to the CPU, fit the wire snugly into this guide before reassembly.
c) align the Num/Caps/Scroll Lock lights with the cover holes properly.

15. If everything is well-aligned and the keyboard seems to fit back properly, replace the screws and tighten them, not too tightly.
16. Plug your keyboard back and start up your PC, test out your keyboard. If it works, good, you're up and running again. If it does not, check if all the parts are in. Are any wires loose? Are the components aligned properly? Did you plug it in the correct port?
17. If your keyboard does not work, and nothing you do can make it, then...
18. Proceed to carry out my favourite method and get a new keyboard.

Happy cleaning!