How must I care for my eyeglasses? Lens paper? Diaper?

Any soft cloth. Any soft cloth can be used. Popular now are microfiber cloths which come with many eyeglasses when they are made by the optician, and these are very effective a removing debris. You can also wet the lenses and use a little liquid dish soap to get off accumulated debris. You do not want to scrape them with anything abrasive.