Try washing it in distilled water and let dry for a couple days and it should be fine. I have done this with both the old and new style wireless apple bluetooth keyboards as well as the wired ones. Do remember to remove any batteries first.

I have heard a few people put theirs in the dishwasher but I never tried that since regular water leaves water marks and can make things worse. Distilled water won't damage any of the components.

Do make sure you let it dry for at least 2 days before putting the batteries back in and do not use a hairdryer.