Great question! Receipts are sent electronically after every payment (Text Message or Email). Your customers will be prompted to enter in their preferred email or phone number.
In regards to shipping address, you can add it as a note to the payment, or if you turn on Customer Management you can add a customer to your Customer Directory to store their information for shipping purposes.
Here's an article that gives a bit more information: http://squ.re/1YxNR42
