• How do I apply the residual value from a canceled non-refundable ticket to a new ticket?

When you cancel all or a portion of a non-refundable ticket prior to travel, the residual value is retained in the ticket number, less the appropriate change fee (usually $150 for domestic fares, $250-275 for international fares). The residual value is valid for travel commencing no more than one year from the original ticketing date and can only be applied to the purchase of a new ticket by the same passenger (formally, you are changing the original reservation rather than getting an actual refund). Be sure to record the ticket number for future reference (001 followed by ten digits; note that record locators expire several days after travel), although any agent should be able to access the information in your AAdvantage account.

To apply this residual value towards a new reservation, put the reservation on Hold on AA.com, then call AA with the record locator and ask to apply the residual value of the old ticket to the new reservation. If the residual value is less than the cost of the new ticket, then you can pay the remainder using a credit card. If the original ticket was booked on AA.com, you will not be charged any telephone booking fees for completing the purchase of the new ticket. If the residual value is greater than the cost of the new ticket, then the remaining value will be refunded in the form of a voucher, which can be applied to the purchase of a ticket in anyone’s name.

The entire rebooking process may also be done by phone or at a ticket counter.

AA.com: Refunds | Refunds FAQ
FT: Have to cancel flight; what now? Refunds, reticketing, validity issues. [merged] (Post #6)