Check your email. Upon purchase of an airline ticket online, most commercial airline companies will send you a confirmation email that includes the dates, times, flight numbers and a confirmation number for your reservation. The easiest solution to finding that information if you've misplaced it is to go back into your email archives to locate this email.
Visit the website for the airline you're flying on. Again, most commercial airlines provide a portal for their customers where you can put in your confirmation number or the credit card number you purchased your tickets on and pull up your flight itinerary with all the pertinent information on it.
Call your travel agent. If you booked through a third party, getting the details of your flight is as simple as a phone call. Give the travel agent you booked with a call and request an itinerary for your flight. They can either email it to you or mail a hard copy in time for your travel.
Call the airline. Use your last name, social security number, credit card number or confirmation number to request the details of your flight from a representative of the airline you're traveling on. This solution is the smart one if you're on your way to the airport and you want to check to make sure your flight is on time.