Confirmation numbers will be found on the final page of the reservation when purchasing tickets online, in the confirmation email or on the receipt and boarding pass. The specific location might vary by airline or booking service.
If the email or receipt has been lost, the customer service number provided by the airline may be able to look up reservation information if given the credit card and customer information was handled over the phone. Confirmation numbers can be used to check in online or at the airport kiosk. They look up the reservation information and allow the customer to print out their boarding pass.