for every day stuff I usually just use a damp cloth or even a damp paper towel, if you need to really get it cleaner than that you can use a bit of alcohol or mineral spirits or even acetone. if it starts to look a bit dry especially after a chemical wipe down then refreshing it with a little mineral oil or any other light oil that you don't mind the odor of, then wiping it down well to dry it well and remove the oil wil leave it replenished and not dry looking
a scotch brite pad can be used if you need to get aggressive with it and remove some scratches but beware that with a scotch brite you are pretty much almost sanding and refinishing it so a little caution is needed there and I would usually say that is a last resort if all the others don't give you what you need. if you do scotch brite it then I'd recommend trying to just wipe it straight in one direction with the grain already there in the brushed finish, and yeah, this is def NOT for polished surfaces unless you no longer want them polished

this is fine to do on satin finishes though. for polished finishes a micro fiber with a little plastic polish can help, similar to the way yu would polish up automotive headlights or tail lights and stuff, products made for those uses would be adequate here too