How should I handle repairing a door ding I know someone caused?

If it's not a serious ding that it is relatively easy to repair on your own or not too expensive to have someone else fill and repaint, then just do it that way and avoid a confrontation. If it's not easy or if it is too expensive to repair, ask the perpetrator if they will pay for all or part of the damage. If they say no, you can sue--but the expense of litigation would be greater than the repair itself.