For a while now, the transit option has been shuttle buses via South Remote to the TRE train (no Sunday service).

Now, DART recently opened the Orange line rail as close as Belt Line Rd. You can take the DART #500 bus from Terminal A (curbside upstairs near gate A10) to the Belt Line Rd station and ride the rail from there to downtown. This may be a little faster (and service a bit more frequent) than the TRE, especially if your flights happen to be using Terminal A. But it's still a schlep.

Target date is December 2014 for the Orange Line to extend all the way to the airport. The station will be at Terminal A. Once open, this will eliminate the extra bus ride.

All the details here:
http://www.dart.org/riding/dfwairport.asp