I tried to do nail marble using one of my grandma's drinking glasses but it didn't work for me. I ended up having to take off the nail polish that was left on the glass. I used nail polish first and then after I washed the cup twice with antibacterial hand soap and then my mom washed it with dish soap. Is the drinking glass safe to drink out of or should I throw it away?
There are two kinds of nail polish, enamel and lacquer. Acetone is sold in little bottles and called nail polish remover, but it doesn't work well on enamel. Use a single edge razor blade to shave the paint off the glass. A double edge blade can be bent to follow the curved glass, but you better be graceful so you don't slice your thumb. Razor blades are sold at hardware stores, and they might have something to dissolve enamel nail polish too.
It's time you learned about google.com so you can search what others have posted on any subject. Go to that site and type "marble nails" in the box. Here is one of the links you get, and she tells you exactly what to use for every step. She specifies a plastic cup, not your mother's pretty drinking glasses.