When you book flights through Duffel, it's your responsibility to send a booking confirmation (usually by email) to the customer.
Duffel will never contact your customer directly, and most airlines on Duffel (with a few exceptions) will not send a confirmation themselves, so it's in your hands.
At the moment, we don't offer an option where Duffel sends the email for you. If this is something you'd be interested in, please do get in touch with us.
A small number of airlines - mostly "low cost carriers" - will also send the passenger their own booking confirmation with their itinerary, and sometimes the price paid for their booking. You can read more about this here.
In the confirmation, you should include information about the itinerary, payment details and booking reference (which the passenger will use to check in).
The API includes all of the details you need to send in that email. Below is a mock booking confirmation email overlaid with all the key data you need to convey to your customer.