I always tell families that the best way to keep their piano clean is not to let it get it dirty. This means instructing everyone to wash their hands before piano practice. Not only is this good hygiene, but if you couple it with putting your child in charge of cleaning the piano, they will develop a sense of responsibility that can't be found with a cheap toy or video game.
If you have a new piano with a shiny finish, it is probably polyester. These piano finishes are the most durable and easiest to maintain, as they are treated very similar to glass. Polyester is very hard and very thick, rounded on the edges, reflective like a mirror, and not so prone to cracking. Cory piano polish is what we use to clean and remove dirt or fingerprints from a piano. We use it in combination with microfiber detailing cloths found readily on amazon.com. Just spray one or two pumps onto the cloth, not directly onto the piano, and gently rub away dirt in the area you want to clean. Move in a circular pattern until you have cleaned the whole area or case part, then flip the cloth over to a dry spot and gently polish again. Once the finger prints are cleaned away, then all there is to do on a weekly basis is dust. If severe damage or cracking occurs, this finish is the most difficult to repair, and you'll want to find a technician who specializes in polyester repair.
If the piano is matte, and I'm talking about flat like the eggshell style water-based house paints, then all you need to do is a gentle cleaning with a slightly dampened microfiber detailing cloth. These finishes are usually the thinnest but show scratches. If damaged, they are the easiest to repair. Many of our clients will touch-up scratches themselves, and even piano movers are skilled in repairing a matte finish.
The last basic finish is the satin hand-rubbed traditional piano finish. This is a semi-durable finish, slightly prone to scratching, and very difficult to maintain like new. Cory does supply a satin piano polish, but honestly, once you get finger print oils on your piano, they never really go away unless you resurface the part. I learned in the trenches of a piano rebuilding shop how difficult it is to achieve this beautiful finish. Lacquer is sprayed and leveled many times to build up the thickness of the finish. Different grits of steel wool combined with lubricants and rubbed in exactly parallel lines for hours give you a very beautiful, semi-reflective, sparkling finish. Believe me, if you have OCD, this is going to give you trouble. The best thing is to use a piano cover and keep your hands on the keys. If a satin hand-rubbed finish is scratched or dinged, it is easily repaired by a knowledgable technician.
Vacuuming your piano is recommended, but it is also a specialized art. Most people never clean behind their instrument, so if you have purchased a used piano, we recommend you have your technician do a cleaning to the whole instrument, front, back, insides and under the keys. Cleanings take between 1 hour and 6 hours, it all depends on what environment the piano was in, and how old it is.
Lastly, you can clean the key tops with a damp cloth, but it's best to have your piano technician do it every few tunings. He or she should remove the case parts so they can clean the back part of the white key that is hiding under the red felt, and the sides of the black keys. That is where the dirt likes to hide. This takes, on average, 20 minutes, but ask for an estimate for severely stained keys.