American flies in and out of Terminals A, C, and D and American Eagle flies in and out of Terminals B and D. You should be on mainline American the entire way. If you are transiting between A and C, expect the entire process to take 5 to 10 minutes gate to gate - if you are going between A and D, it will take 10 to 15 minutes - and if you are going between C and D, it will take 15 to 20 minutes. (Those times based on my personal experience and they can possibly be shorter, but that's what I typically budget for myself.)

If for whatever reason you are delayed coming in from San Francisco, ask the flight attendants before you get off the plane which way they recommend going - most of them are also used to making tight connections at DFW and can give you best advice. As well, American will announce gates for your San Antonio flight before landing in DFW - and there is a terminal map in the back of the inflight magazine that will help you visually plan out your journey before you hit the ground.

With any luck, you'll land or depart from the newer Terminal D and have enough time to stop for food - the best restaurants in the entire airport are in that terminal and its a pleasant place to spend a layover.