Learn to ride the 4-wheeler really well. You should get really good at riding your 4-wheeler without doing anything tricky or trying any stunts. Often, when you purchase your 4-wheeler, your dealership will offer a training course. Take it. Additionally, drive your ATV on flat ground, bumpy ground, hills and other terrain until you are REALLY good at driving it.
Ride your ATV on a ramp or hill. Get a feel for what the 4-wheeler feels like when its tires are off the ground. By doing this, you'll experience a bit more of what it's like to ride a wheelie, but with a safer way to start.
Pop the front end up. Let it back down. To do this, as you're starting out, hit the throttle really, really hard. As the 4-wheeler accelerates quickly, the front end will be thrown up. As it comes up, let off the throttle to bring it back down to the ground.
Practice. As you've learned to bring the front end up, practice by sitting at different angles on your 4-wheeler to produce different effects. As you hit the throttle, pull back on your handlebars to bring the front end up even more. Ride your 4-wheeler as far as you can with the front end up and on the back two wheels. To let it back down, just let off the throttle.