New balls would be my first suggestion. If that doesn't do it, I would a small amount of all purpose cleaner (simple green is what In use) and then follow that up with water. I use microfiber rags and lots of elbow grease.
I have owned some tables over the years that just had a slick playing surface. Not much you can do about that other than selling and buying a different one. Newer tables are less prone to this issue in my experience.