If the activity already started (or the customer is allowed to sign up later after the activity start date) you should set the 'Start reg time' as todays date (you can just punch in 'now') in order to reflect the actual start time for the customer and possibly adjust the price.
Leave the 'End reg time' empty.
On the row containing the new registration you either click for e-mail or paper invoice to the customer. (Note: If you choose to let the customer pay cash or with a credit card not linked to KeepTrack you will have to register the payment under in order to avoid wrongfully billing the customer again.)
Or you click for point-of-sale with the customers choice of payment option on file. Via POS a receipt is automatically mailed to the customer (and the payment is automatically registered under 'Payment').