Everyone wants to go fast. When I first started biking I had to fight every urge in my body not to take off downhill as fast as possible. Luckily I started riding with a much more experienced rider who forced me to practice braking. "You've got to learn to walk before you can run" he would say. It seemed so foreign to me, to practice braking on a bike but my friend assured me that brakes stop you but they also help you adjust your speed when taking a turn. Not to mention the better control you achieve by using your hands to stop yourself.
Hedge the top tube and place your hands on the handlebar. There are two levers on each side that stick forward. To brakes for the front of your bike sit at your left hand, the this may seem odd if you are used to coaster brakes. The lever should not get any closer than about an inch away from the bar. Now gently squeeze the brake lever take notice of the brake pads clamping down on the front tire. They should catch the wheel but not go below the rim or hit the sidewalls of the tire. Your right hand controls the rear brakes, inspect them as well. Don't be alarmed if your breaks squeak quite a bit until they are broken in, if that squeak does not go away then you know your brake are unaligned not positioned correctly on the rim.
Learn To Walk, Then Run
After I practiced enough and my friend deemed me "worthy to ride" I quickly discovered how easy it was to brake going uphill but not so much when speeding down a trail. I did have a few moments initially of sheer terror, almost crashing quite a few times but thankfully I listened to my friend and avoided crashing.
You should only apply the brakes in the proper positioning. Balance is key, adjust both your weight and hand positioning to achieve balance. Stand on both pedals, put one foot forward making sure the pedals are parallel to the ground. Keep your butt roughly an inch about the seat with your thighs in tight.
The hands should be balance as well. Keep your thumb and forefinger on each hand firmly wrapped around the handle bar. Your three outer most fingers should rest on top of the brake and always be ready to stop at all times.
Get yourself into the set position by slightly bending your arms at the elbows. Slowly glide in this position, squeeze the rear brake ever so slightly until reaching a gradual stop. Then, slowly apply the left brake. You should notice that the front brake gives much more stopping power due to your weight being behind the brake as apposed to being in front of it. Improper use of the front brake, for example, squeezing too hard can send you flying over the handle bars. While to much pressure on the rear brake will cause you to skid out of control.
When needing to stop suddenly obviously you will want to use both in conjunction properly to avoid any accidents. You should definitely get your "touch" down pat as far as how firmly your brakes need to be applied. Practice slowly riding in the set position and gradually squeeze the left and right brake at the same time. You should notice that you will be able to stop rather quickly. Always keep your body weight low over the seat.
I did not realize how taxing stopping could be. On a long downhill your hands can get very tired and start to cramp. As if mountain biking wasn't difficult enough!