How do owners come up with what to charge for HOA fees?

In most cases the HOA has to have a budget prepared and the fees are based on that budget. If you are in an HOA and you are questioning the fees, contact the HOA to see a copy of the budget. It should be available to all members.

The same way any organization determines how much to charge. The same way your government determines how much to tax you. They figure out how much they need to spend for the year and divide that amount over the units in the association.