If just a simple in store sale and the customer is gone, you can go back into the transaction and at the top of that transaction (when you open it) it'll say "Send Receipt" and you enter email or phone number.
During an in store sale where the customer is still there you would enter the cash amount (towards the top of the page after you hit the ring out button) and then a screen would pop up for email or text or no receipt.
If you are talking about something else you could send an invoice but you can't mark it as paid until after you send it (Square please fix this). However, once you send it, you can then mark it paid by whatever method fits and it will send a paid email.
