I've come across this several times in the past few years so thought I would mention it to the ladies who are just beginning to mountain bike. The bike you rode as a child and perhaps the cruiser type bikes that you have ridden are designed to allow you to stop the bike with your feet flat on the ground while sitting on the seat.
If you are on a mountain bike, you should not be able to put your feet flat on the ground when you are sitting on the seat. If you can do that, your seat is far too low and you will wear yourself out trying to pedal with your knees up around your ears (and an improperly adjusted seat can cause back pain, etc as well).
A rider just starting out (or a rider on a particularly technical trail) might want a slightly lower seat height initially but in general, with someone holding the bike and your heels on the pedals, if you pedal backwards slowly your leg should be pretty much fully extended when your pedal is at the lowest point.
If you adjust your seat properly, you will probably need to practice starts and stops if you are used to starting and stopping seated on your bike, so practice in the parking lot for a few minutes before you head off down the trail.
And please, any of our experts out there please feel free to jump in and add some extra advice related to seat height.... I just know that a properly adjusted seat is very important.
Saddle fore/aft position is also important. Here's a few links on bike fit with some decent info. Everyone has their own theories of how a person should sit on a bike, and everyone's body is different, so play around with your position and see how you feel.
Don't forget, if you move the saddle forward or backward it changes the distance to the bottom bracket, so if you want to keep that distance the same, if you move the saddle back you'll also need to lower it some, and vice versa.
I've had a BG Fitting from Drew at Andy Jordans and HIGHLY recommend it. He moved my cleats back towards my heels, moved the saddle much further back (so much so that I had to get a different seatpost), and raised it just a bit. The difference was night and day, I can put down more power more comfortably. Moving the cleats made a big difference, out of the saddle feels so much better, my calfs have to do less work to stabilize my ankles, so I feel much more connected and solid on the pedals.
If you're just starting out there's no need to see someone for a professional fitting. But if you're serious about the sport it's worth considering, especially if you have any knee or back pain while riding, they can help correct that.