Establish your reason for requesting the refund, and read the fine print about refunds on your e-ticket or paper ticket, and on the airline's website as well.
Gather all of your airfare information in front of you, including the flight details and cost of your ticket, as well as your credit card that you used to pay for the ticket. Know what you are ready to accept instead of a full refund, such as a travel voucher that would give you a discount (amount varies) on your next ticket purchase.
Call the airline or travel agency website where you booked your ticket and be clear and firm about your reason for requesting a refund. As mentioned in the article, "How to Get a Refund When Your Airfare Drops," you may have to call several times before you speak to someone who is willing to work with you and actually knows the airline's policies in detail.
If you find that your situation is still being ignored by the airline or travel agency, feel free to write a letter of complaint to a travel publication such as Budget Travel, who will act as your mediator if the editors choose to help you with your situation, publish all correspondence with the airline, and attempt to get you the maximum amount of compensation possible.