Cleaning even the dirtiest piano keys is much simpler than you may think. There are rarely any special chemicals or tools needed, and particularly with most modern plastic key tops, there’s very little you could do to harm the keys.
I would always recommend starting with the least abrasive cleaner possible. Quite a lot of cleaning can be accomplished with just a damp cloth. In the picture below, I did all of the cleaning with a multi-surface furniture cleaner spray, along with some paper towels.
On ivory keys, more care should be taken, not so much because typical household cleaners will damage the ivory (just test on an inconspicuous spot first to be safe), but because the ivory keys are much easier to chip if you’re not careful around the edges.
With a little common sense and some elbow grease, most piano keys can be cleaned quickly and safely!