How does athletes foot spread person to person?

Contact. Athletes foot is a fungus. It spreads by contact. Usually with a contaminated surface like shoes, damp shower floor, mats, swimming pool, etc. Best way to avoid spread is to treat surfaces and don't go barefoot in public areas.
Contact. You share socks, shoes with others. Your feet closely contact with others' feet. You walk on the floor with barefoot and the floor happens to have fungus growing there.