Turn off the device to which the keyboard is attached.
Dampen a cotton cloth with rubbing alcohol.
Rub gently across the keyboard with the dampened cloth. Rub across the entire row of each row of keys in a horizontal manner. Let the dampened cloth touch each key as it passes over it. Rub down the rows of keys vertically, using the same method.
Dampen the cloth again when it gets dry. If it's wet enough, the cloth should leave a light sheen on each key. Examine the keys. If you still see finger marks on the keys, wrap the dampened cloth around your index finger. Place it on the key and twist your finger around, in a back-and-forth motion, focusing on individual keys that need extra attention to get them clean.