Greg,
My husband is director of the local Mountain Bike Patrol and I used to mountain bike with him, but haven't for a few years.
My suggestion is to start out on dirt roads rather than single-track trails. You have a lot more leeway for error on dirt roads - and they tend not to be as technical as single-track (unless they're 4WD roads, which can be pretty technical even for bikes in canyon country.)
When you feel comfortable on dirt roads, move on to the "easy" single track trails. By "easy", I mean those trails which are relatively flat, not too (loose) rocks and not too many tree roots. Beware: trails which have a deep furrow are intimidating when you're first learning because keeping your front wheel within the 12" or so that the trail gives you can be tough until you get used to it.
Visit a local bike shop and get some recommendations for beginner trails. Most bike shops have maps available and personnel who know all the trails in the area. They're a great resource.
Don't feel like you have to ride the entire trail!! GET OFF AND WALK through the tough sections that you don't feel ready for.
Not sure how much of a cyclist you are (if you cycle a lot, you probably already know this), but when you're going DOWNHILL, get your butt up off the seat and push it WAY back to move your center of gravity further back on the bike. The steeper the grade, the more you want to get your weight back. (I remember sometimes having the seat pushing into my stomach.) If you don't do this, you'll feel like you're going to go over the handle bars - and very likely will. Practice doing this even on easy downhills so that you get used to the feel of doing it.
Use your low gears when going up hill!! It's much easier on your knees to "spin" rather than pump the pedals really hard on the uphills. And as you get more technical, the only way to go up some of the steeper inclines is in "1-1" (smallest gear in the front and largest gear in the back.)
Be respectful of other trail users. Bikes are supposed to yield to BOTH hikers and equestrians. If you see a horse on the trail, stop, pull off and greet the riders verbally so that the horse will know you're a person. If the horse is not used to bikes, it might not recognize you as a human if you're straddling your bike and might spook.
Don't go faster than you can control the bike. This is especially important when going down switchbacks on trails shared by hikers. If you are coming up on a hiker from behind, slow down and let them know you're there - and which side you'll be passing them on. Give them time to react b/c you might startle them and even if you say "Passing left" - they might move to the left in a panic.
MOST IMPORTANT: WEAR A HELMET AT ALL TIMES!! Also, you'll want to have toe-clips on your pedals so that your feet don't slip off the pedals, esp. going downhill (when your only contact with the bike is your hands and feet, b/c your butt is off the seat and pushed back.)
Oh - and always bring a patch kit (or spare tube) and tire irons, and know how to change a flat tire. You don't want to be stuck out on the trail and have to walk all the way back home (or to your car) carrying your bike.
Be sure to bring plenty of water - esp. since you're in an arid climate. This is esp. important in the heat. I find that I stay more hydrated with a Camelbak (or similar) system because it's easier to drink while continuing to ride than having to reach down for a water bottle.
This might be more than you wanted to know, but should help some. You might want to take a beginner mountain bike class to learn some of the techniques of riding that will make the trail riding more enjoyable. But, if you start out on dirt roads, you'll still get a good workout without having to worry so much about the techinical details.
The other MOST IMPORTANT thing: HAVE FUN!!
Jeanie