Dampen a microfiber cloth with >90% isopropyl alcohol and wipe down the entire surface of the keyboard, paying special attention to the space between keys, and areas that are noticeably grimy.

Isopropyl alcohol that is >90% pure is generally free enough of impurities that it won't damage sensitive electronic equipment, but it's still a good idea to be careful with it! The cloth you use to wipe the keyboard during this step should be damp, not dripping wet.