They make a special sponge like wiper with cleaning fluid. I'm sure it's still available...if not, rinse with warm soapy water, then clean water, then air dry. A hand held hair dryer set to cool works well
Mild dish soap and water on a clean sponge - nothing abrasive. Wipe in the direction of the grooves. You don't need to wet the label, you just want to get the dirt and grease out of the grooves. Be sure to rinse it well. You can dry the platter with a soft dish towel, but be sure to let it air dry for a while before you play it. The towel won't get to the bottom of the grooves.
There are many schools of thought. Some use cleaning machines. Others use soap and water. Some cleaners leave residue. Experiment and see what works for you