You would send a copy of your zine to a distro. If they like it, they will contact you back and order anywhere from 5 to 50 copies of your zine at a wholesale price. Some distros also do consignment. Then the distro owner would add your zine to their website or catalog for people to order, and sell it at a retail price. That's it in a nutshell.
Most distros do not do the photocopying (that was more common many many years ago). You would copy the zines yourself and sell them to the distro at a wholesale rate. Many of the distros go about 50/50. So if you wanted your zine to be sold for $1, then the distro owner would pay you .50 for each zine. The little bit of money the distro makes goes into buying new zines for stock and website expenses, advertising, zine fair table fees, etc.