What is the best way to get from San Antonio to Chihuahua, Mexico to take train to Copper Canyon, and what airlines fly down there from either Austin or San Antonio?

I don't think you can take a train. I would think a local bus company will take you down. Used to be a tour company called Armadillo tours. Why don't you look under AltaVista yellow pages for a travel agency with an 800 number in San Antonio and ask them?

Do you feel like driving? Or would you rather get there fast? If you decide to drive, you have a couple of options: You may take I-10 west to El Paso, cross the border, and drive south to Chihuahua. Or you may take I-35 south to Monterrey, then to Saltillo, Torreon and then to Chihuahua. That should take around 12-13 hours of driving.

The easiest (and most expensive)way may be flying to Monterrey (in Mexico) and taking a plane from there to Chihuahua. The second easiest may be to fly to El Paso, rent a car there, and drive 3 hours to Chihuahua.

American flies into Monterrey from DFW; not sure if they do from austin or san antonio but if you don't mind backtracking a little you could get a connection through dfw from either.

Have you checked Continental Airlines? They are Texas based and have pretty broad coverage in Mexico/Latin America.