While events and classes are designed to let customers book and pay online, you can manually add attendees.
When this is done, you will need to manually invoice them for payment which is why it is encouraged to rather share the event or class link with them for joining.
Click on 'My Business' and then on 'Events / Classes':
On the right hand side of the event or class, click on the options menu and then click on 'View / Add Attendees':
This will let you type in the name of the client to add, or remove clients that have already registered for your event or class:
When an attendee is added, the event or class gets added to their account. From there, you can send them an invoice or capture a payment.