Thanks for the question. This is something I actually have some knowlege on (probably just enough to hurt me but some knowlege none-the-less :-)
I'm presuming this is your classic gift card for $20, $50 $100 or whatever dollars that you can take to a store or stores in exchange for Dallas Cowboy merchandise.
Since your username suggests your are a Redskins fan (I'm an Eagles guy) I can completely understand your dilemna.
Gift cards generally do well on Ebay. Open an ebay account if you do not have one and attempt to auction it. Ebay now allows up to 50 (or maybe 100?) free auctions a month so it won't cost you anything but time to list. You'd only pay a PayPal and Ebay fee if it sells.
Be sure you take a photo of the gift card but take the photo so that any on-line codes or numbers (if any) can not be clearly read (people steal on-line codes, from pictures)
Post the gift card and be sure to note all the disclaimers, value, and every detail on the card except any codes.
When you post the gift card, I'd suggest posting it for a significant amount of what it is actually worth. If it is a $100 gift card for Dallas merchandise at any sporting goods store, for example, post it for what you'd like to get for the card. I'd actually try 3/4 of its value at first ($75 on a $100 card, or $15 on $20). If that doesn't sell, you can repost it again at the same price and see what happens or lower it.
I'm astonished at how well some gift cards sell. Some sell for like 90% of their value, some are a dud. Some Starbucks $20 cards I've seen sell for $19 (which doesn't seem worth it to me as a buyer but for a seller who gets the card for free that's pretty good)
I haven't sold sporting goods cards but I would think with football in midseason it would be a good time to post it.
I hope that helps.