I would not suggest just throwing the whole keyboard in the dishwasher, there are parts to a keyboard that can be a bit sensitive to thin films of soap or wetness in general.
If you really want to do this, I completely agree with battlemarz that you should open the keyboard and just wash the parts.
When I do this I first remove the key plates, (most PC keyboards I have encountered have these) and put them on the bottom rack of the washer, right above the jets. They usually will come off easily and all of the keys will be set in the plate so they wont fly out when they are in the machine, (note: you might have to go top rack if your keys are held weakly or if you have monster dishwasher jets). I also throw the little silicone bubble things into the silverware catch basket with the mesh lid on it, and perhaps even the outer housing if I am feeling particularly obsessive.
You do not want to put the dual layer of contact sheets into the wash (usually a clear plastic with silver wires), Because even a super thin soap film can cause errors in key press registering if you type lightly. I usually wipe these down with a damp fine cloth (read: no soap, no toilet paper). You also really don’t want to put the controller board through the wash (the board where the USB comes in… or any circuit board you find in the board for that matter.) and unless you know what you are doing you probably want to avoid getting it wet.
If you do put the silicon bubble sheets in the wash, make sure to stop it before the drying cycle… I don’t know if it will get hot enough to melt the silicone, but it is better not to take the chance.
Also: After the wash is done make sure you wait until the parts are super dry before putting them back together or plugging the thing in.