In the Airline Reservation System, the process begins when the user logs into the system and searches for available flights. If flights are found, the user selects a flight, enters passenger details, and proceeds to payment. If the payment is successful, a ticket is generated and sent to the user's email. However, if the payment fails, a failure message is displayed. If no flights are available, the system informs the user that no flights are found. The process ends once the ticket is sent or an error message is displayed.