The basic order flow is something like this:

1. Customer places an order, you will be informed via email (make sure you have yourself in the Bcc list in stores > configuration > sales emails > send order email copy to)
2. If your payment method has captured the payment, the order will be automatically invoiced. If your payment method has not, before you ship the order go to sales > orders > click the order and then click the invoice button.
3. Go to rentals > send rentals when you are ready to ship (or checkout) the rental
4. When the rental comes back go to rentals > return rentals and return it