I had to hike all day up the Rim and camp overnight in order to shoot the sunrise, sunset and night shots, but it is worth it. You can look hundreds of miles into Mexico.
As digital sensors have improved, it has opened up a whole new world of night-time photography, and you can get images you could never get with film. This image is not bad, but I could really nail it now with my current camera and some tweaks. In hindsight, I really underexposed this image.
Basic formula is simple. Use a very wide angle lens. For aperture, usually f/2.8 or f/4. Set your ISO anywhere from 800 to 2500+ (higher ISO is great if you camera can handle it). To get pin-sharp stars, you leave your shutter open based on the Rule of 500 (divide your focal length into 500 for your exposure length). For my my 16 mm lens, 500/16 = 30 second exposure. Any longer than that and your stars will be blurry. There are tons of free tutorials on the interweb, too.
Tree, agave and stars on South Rim of Chisos Mountains, looking into Mexico, Big Bend National Park, Texas, USA. Canon 1Ds Mark II. 16mm. ISO 800. 30 seconds at f/2.8. If I was shooting this today, I would probably try shooting it at an ISO of 2000 or more to really get the sky and stars to come out.