Dishwasher?!? D:
I would get a tub that's big enough to hold the mainboard, clean it with soap and water and rinse it with distilled water.
Then I would wait for the tub to dry (let it air dry, do not dry it with a towel or something!) and inspect it for spots. Distilled water will not leave spots when it dries, so if you find spots that means there's some residual soap/dust in the tub, which can potentially short electronics, and you'll have to wash the tub again.
Theoretically electronic devices can operate underwater, so long as the water is pure H2O. Ions like iron, sodium and potassium that are commonly present in tap water are what cause shorts. What you are doing here is decreasing the chances that the mainboard will be shorted out after drying.
Now that the tub is dry, put your mainboard in it and cover it with distilled water. Let it sit for a while, you want as much of the electrolyte on the board to dissolve as possible. If you have a means of warming the distilled water without contaminating it then that might help the electrolyte dissolve. (Don't go nuts though, I'd suggest a temp of between 100 and 120 degrees F.)
After the mainboard has sat for awhile remove it from the distilled water/electrolyte solution and let it dry someplace safe. Again, let it airdry; do not use a blowdryer or something to speed the drying process! If you live someplace with tons of humidity you might want to put the mainboard in a static free bag with a desiccant of some type to soak up the distilled water; rice works well. Let it dry for several days, you want the board to be completely dry before you put it back in your Mac!
After the mainboard has dried you might want to identify the electrolytic caps in question and either remove them yourself or have a friend with surface mount soldering experience remove them for you. If you are able, try to identify the etched traces on the mainboard (if any) and repair them. Then replace the caps. (The earlier suggestion of tantalum caps is an excellent one.)
Once that's complete, put the mainboard back in the Mac, reconnect everything, apply power, turn the sucker on and cross your fingers. Good luck!