The bunny hop is the most simple way of jumping a bike: both wheels off the ground at once. Unlike the wheelie, there's no pedalling involved. Most who try to do a bunny hop on a bicycle, though, don't realize the key motion involved in the lifting up of the back wheel. In fact, many who are quite successful at the trick don't even realize they are doing it. Assuming you are not wearing clip-in pedals or cages, the trick lies in your foot's grip on the pedal, not necessarily weight transfer. Here's how to get it right:

1. Find a relatively flat surface, and start coasting. You should be standing up (out of the saddle) with equal body weight on the front and back wheels. This position should situate you a bit farther forward than a normal riding stance.
2. Drop into a crouch, bending your elbows and knees. You are "winding up" for the hop
3. Jump straight up, keeping your weight in the middle of the bike
4. When you are at the point of your jump where your knees are almost straight and your weight is no longer being supported by the bike, lift the bike into the air using the the pedals and handlebars. Most of the weight should be lifted by your feet. Do this by tilting your foot forward so that it is more vertical, pushing back against the pedal. This should give enough friction to literally pick up the bike with your feet.
5. Land with the back wheel first, or both at once. Don't let your front wheel touch the ground first. It will create ugly scenarios later in your biking career.
6. Pat yourself on the back for a bunny hop well done!

There you have it. Although the bunny hop is fun to do, it's only useful on the trail if you're moving quickly. To jump higher and more efficiently, learn how to J-Hop.