Wheelies are an old trick that goes back at least as far as roller skating does and most likely much further. It seems that any time any body has a vehicle with four wheels they need to find a way to make it run on just two wheels for a while. The list of examples can vary from muscle cars to skateboards to quads and motor bikes.
Wheelies are not a trick limited to vehicles with more than one tire. The definition of a wheelie has now extended to include things such as snowboards. While a snowboard does not have any wheels on it, principal of how a wheelie works is exact same.
When it comes to snowboarding, a wheelie is a simple matter of balance. Your goal is to learn how to balance your weight on nothing but tail of your snowboard while going down a slope. As with most skills, this ability also increases your skills required for other tricks.
The exact technique required for you to wheelie will very depending upon your riding style. Of course first step is to be riding down a gentle slope that you are very comfortable with. The first wheelie to practice is tail wheelie where you will be raising nose of your snowboard off ground and riding on just tail.
To raise nose off ground you need to stiffen your front leg, as it will act as fulcrum for you. As you stiffen your front leg slightly bend your rear leg and begin to raise your front leg up into air while leaning backwards. An important thing to keep in mind is that your spine must also bend in a gentle curve to help you arc nose of your snowboard off ground. Once you get nose of your snowboard off ground it is only a matter of learning to feel flex in your snowboard and thus learning what it needs to get your wheelie higher off ground and for longer periods of time.