For one I pay per term, which is 10 lessons. Occasionally we miss one, she usually offers to make up, but if it's our fault then that's nice of her but she doesn't have to.
For the other she gave us the choice as to how to pay. We could pay termly, half termly, monthly or lesson by lesson. If we give 24 hour notice of not being there we don't pay, is the official rule. Having said that I've only once given less than that notice (sick child) and she didn't charge us.
I choose to pay half termly. She then writes her dd's book each week "1 of 6" at the top so I know how many I've paid for, and how many are left. When I pay the next half term, any fees left (or occasionally if I've miscalculated/extra lesson for some reason, outstanding ) I alter the next half term accordingly.
Both require the payment to be before not after, which is perfectly fair enough.