Most of my clients pay in advance using my booking system to get the best possible price. It accepts all major credit cards using processing by Square.
With special arrangements, payment is due at the time of service. This works best with packages, like a pre-paid package deal for a fixed number of sessions. I do that from time to time for things like smoking cessation or weight loss where I know that several sessions are going to be required, but in most cases, it's payment at the time of service before each session.
I accept cash, check and pretty much every major credit card you may have.