I'm in a competition where the race number is written on the back of my hand. Afterwards, with hard scrubbing and soap the marks are eventually removed, but not until my skin is rubbed raw. Is there another way of removing sharpie marks without hard rubbing?
Before you go to the event, make sure you use hand cream (or if not available, any cream meant to use on the skin) and allow it to be taken in by the skin completely before written on.
After the event, normally wash your hands with soap and the marker should get off easier. If it is not enough, apply cream again and scrape it off as soon as it gets some ink in it. In very bad cases you may have to use much more cream than usual, but if the skin was prepared you should get the ink of fast enough.
If you prefer you can also use oil to remove the marker, food quality or to be used for babies by preference for your health but any oil will do if your skin was prepared before the marker went on.
This also works for printing inks and bicycle chain grease, so likely for most sources of dirty hands.
But at work I do use a garage soap like Swarfega if a different local brand, as @Tetsujin mentioned in a comment.
The other two answers are very good. I also want to comment that permanent marker will vanish within a few days of normal hand washing. The ink only colors the outer layer of skin (epidermis), which constantly sloughs off.
(The OP did not mention removing the ink immediately. It's natural to infer that from the question, but it's not actually part of the question.)
Use rubbing alcohol combined with scrubbing and soap. This gets it off faster. If nothing else helps, use nail-polish remover (also known as acetone) and wash it off with soap and water.