Ivory piano keys should not be drenched in water as this can damage the ivory and cause the keys to swell, making them harder to play properly. Do not use a brush or scouring pad on the keys. A soft clean cloth will work just fine.
Only use a very small amount of soap. You do not want the cloth to be drenched in soap or be lathered with soap. If you do not want to use soap, you can skip this step. Often marks and fingerprints will come off the ivory easily with just a damp cloth.
If there are stains on the keys, you may need to use a stronger cleaning solution like rubbing alcohol, milk, or toothpaste to remove them.
Once you have wiped all the keys, use another clean cloth to dry the keys. Make sure there is no excess rubbing alcohol or water on the keys, as this can damage them.
Check that the toothpaste does not contain any coloring or dyes before you use it. You do not want to end up dying the white keys or making them more stained with the toothpaste.
Never scrub the keys hard with any cleaning products, including milk. This can end up damaging the keys.
Apply the diluted cleaner on the keys with a clean cloth. Do each key at a time from top to bottom. Then, dry each key well with a new clean cloth, making sure there is no excess cleaner on the keys.
There is a risk that you will damage the ivory piano keys with the ivory scraper if you use it incorrectly. If you are not sure how to use the tool properly, reach out to a professional.
Getting a thorough cleaning done on the keys once a year by a trained technician may be a good option, especially if you use the piano often.
You can also get in the habit of wiping the keys with a dry clean cloth after you done playing the piano. This can keep dust and dirt off the keys.
If the piano is not used often and you want to protect the keys from damage, you can get a long key cover to go over the keys or put down the key cover on the piano. Keep the keys covered until the piano is to be played.