Coins (specifically a type called an obol or obolos) were left on the body or placed in the mouths of the dead.
The dead give Charon the coin, which shows they have had proper funeral rites and therefore deserve to be transported to Hades.
The Aenid by Vergil, Chapter 6 has this to say
> Why some were ferried o'er, and some refus'd. "Son of Anchises, offspring of the gods," The Sibyl said, "you see the Stygian floods, The sacred stream which heav'n's imperial state Attests in oaths, and fears to violate. The ghosts rejected are th' unhappy crew Depriv'd of sepulchers and fun'ral due: The boatman, Charon; those, the buried host, He ferries over to the farther coast;
Despite having neither coin, nor being dead, Heracles managed to cross as did Orpheus and various other heroes.