This is an excerpt from Mastering Snowboarding by Hannah Teter & Tawnya Schultz.
Understandably enough, one of the first things people want to know when they're learning how to snowboard is how to stop. First of all, it's not by sliding and sitting (or maybe slamming) on the ground. Stopping is a motion controlled by the heel- or toe-side edge of your board. Just as with getting up, there are two ways to stop. The easiest way to learn the first method is by doing it. Begin by standing on a gradual or beginner slope with your entire body facing downhill and your board across the incline. Stand with your knees bent, and stay low. Don't think about trying to turn yet. Concentrate on what edge control and stopping feel like. If you're standing on a slope, you will immediately begin sliding down the hill. Think about pressing your heels into the back of the board and lifting your toes very steadily off the ground. People always mess this up and completely flex the foot. It isn't about flexing; it's about pressing. Your board will be doing a lot of the work, but always remember you are the one in control. Now practice sliding downhill while remaining in that position, with your whole body and board perpendicular. Pressing your heels hard into the snow is what is going to make you stop. You will feel yourself slow (figure 4.4).
There is no doubt you will probably fall quite a bit learning how to stop, but this is where all the pretraining and techniques for getting yourself back up come in. Your legs are sure to burn after practicing this for a while. It's like staying in a squat position for a very long time. You may experience some cramping. If so, sit down and stretch out your legs. If the pain is persistent, take a break off your board and shake out your legs.
To learn the second method, the uphill stopping technique, start by using the belly method to get into a standing position. With your entire body facing uphill and your board horizontal, push yourself off the ground and stand. Make sure you have plenty of room for this technique. As noted, you should always be aware of what's below you first and foremost, and this is difficult to do when you are facing uphill.