Starting tomorrow, AT&T will be offering a new trade-in program to customers that gives them at least a $100 in credit when they bring in their old smartphone in favor of a new one. This means that as long as you are willing to part ways with your older device, you can get at least 50% off a new smartphone priced at $199.
The Samsung GALAXY S 4, BlackBerry Z10, and HTC One are all priced at $199, so if you were to trade in your old junker, you would only be paying $99 for one of these phones. Furthermore, for mid-range smartphones that are priced at $99, you'd be getting these for free if you traded in your old phone.
In order to get a trade-in value for your old phone, you'll have to answer some basic questions about the condition of it first, including functionality as well as if anything is broken. Then you have to enter in the device's serial number and the phone number of the phone (it has to be an AT&T number). Once that's done, you'll be able to see how much your old phone is worth.
Then again, you're probably still better off using another service like Gazelle, Swappa, or even eBay. You'll most definitely get more money out of your old device, and depending on what service you use, you can haggle with the price in order to get the best deal possible. At that point, you can take that money and get yourself a brand new phone.