Editor's Note: Bumped to the front because EPHokie did a great job putting this guide together. If you're making the trip to El Paso and have questions, she might be able to answer them in the comments.
Safety first, kids. Don't go to Juarez. Just don't. I don't care what you've heard - NO. Also, visiting Lower Valley (far East side) isn't a great idea, nor is driving Paisano after dark.
El Paso is located in the high desert - the elevation here is 4000+ feet above sea level. For those of you who live at or near sea level, it's not going to be fun when combined with the low humidity. Drink a LOT of water. Really. Bring a refillable bottle of water and keep it topped off all day, every day. Also not fun at this elevation is the sun - if it's at all sunny, please wear sunscreen. You will burn much faster here. Finally, the lip balm of your choosing (I'm a Burt's girl, myself) will be greatly beneficial. (Also, if you're prone to nosebleeds or are sensitive to low humidity, consider asking your hotel for a humidifier to put in your room. It'll make life so much nicer.)