Hey there L. Thanks for the note here, and for your interest in our plugins! There aren’t any built-in payment options for the plugin, at this time. Instead we rely on these add-on plugins that each have their own method of handling purchases.
We’ve got two add-ons related to ticketing: Eventbrite Tickets and WooTickets. Eventbrite Tickets handles all payment processing through Eventbrite; this means it’ll work with Paypal or Google Checkout. WooTickets integrates with WooCommerce for payment processing. Out of the box that means Paypal will work, but I know WooCommerce has a number of additional payment gateway add-ons themselves (ie Stripe integration) too.
All that to say: you do have a few options. But none of them are specific to the core calendar, and they will require a ticketing component to work.
That help? Let me know if not, and I can adjust my reply as needed. Thanks again for your interest!