A wheelie is a relatively simple bike trick that consists of the rider pulling the front wheel off the ground and balancing himself on the rear wheel, all while in motion.
To perform a wheelie, get up from the saddle and pedal forward while pulling hard on the handlebars. Put the bike in low gear to help with the pedaling part. While the front wheel is in the air, maintain an upright posture and lean around to control balance - do not hunch over the handlebars. For added control, tap the rear brake (forward balance) or pedal forward (rearward balance).
With enough skill, a wheelie can be maintained indefinitely. To complete the move, lean forward and allow the front wheel to drop back to the ground. Ensure it is straight on contact, or you may lose control of the bike.
Safety
Leaning back too far (i.e. as a result of pedaling too hard) will cause the bike to fly out from under the rider. Although most people will instinctively hit the ground running, practice recovering from this event before attempting an actual wheelie.