I set up a registration form, how does the payment work?

Since you're using the Purchase Order payment tool in your form, it will not capture real payments which means the form will be submitted normally. This is useful when you are collecting payments manually offline like Check or Cash.

If you want to collect payments online, you can replace the Purchase Order payment field in your form with the other payment tools you like, e.g. Paypal (Standard), Stripe, Square and etc.

So basically the user has to fill the form, select a product or subscription, enter their payment credentials on the form and when they click the submit button, they will be charged right away. Some of the payment tools would also redirect to its payment gateway like Paypal Standard which would redirect to Paypal's checkout page where the user pays the amount.