Here is a long answer from another site.
"The most common bunnyhop is done when you ride along crouch down and shoot straight up and lift both tires off the ground at the same time. Of course, NOBODY good does that. Below is what is the standard freestyle bunnyhop- it was referred to as a bronco because it kind of looks like that when you do it. But if you call it anything besides a bunnyhop people will look at you funny. (he-he)
Begin by rolling at almost any speed- probably a good speed to learn the trick is slow/medium so if you case it you won't die.
DO THE REST OF THE STEPS IN A VERY QUICK SMOOTH MOTION...
Lean down and back on the bike- slightly behind your seat. Pulling back on the handlebars to get the front wheel of the bike off the ground. The higher you can get the front wheel at this point the higher you will usually be able to go... NOTE: If you pull back or lean back to far the bike will loop out and you will fall on your butt. NOTE: This is just like pulling up for a wheelie!
Make SURE your weight is back when you try this next part. If your weight is to far forward you will nose dive and could even go OVER the handlebars...
When the front wheel has peaked out shoot your body straight up and a little bit forward. Do this by pushing down on the pedals and pulling on the bars. In a split second your weight is travelling upwards. BASICALLY YOU ARE JUMPING. With the front wheel in the air already you do not have to lift the full weight of the bike when you end up lifting it. But you must lunge (jump) upwards as quickly as possible. This will REALLY affect your height.
As your body is now travelling upwards, lock your feet against the pedals (see note below) and lift the bike off the ground. HUH? How do you lift the bike? By pressing down and slightly backwards on the pedals you can grip them. You don't put your WEIGHT on the pedals... you have your feet at an angle and pull UP with your feet. This is the HARDEST part of the trick. Do NOT think it will come in a day... or even a week. Once you can do it do NOT expect to be able to get a foot of the ground... MAYBE a few inches... But height will take practice...
To get really high.... Because you have extended your legs when snapping upwards you should bend your knees and tuck the bike in as close to your body as possible to get the maximum height.
Riding out isn't a problem- just let gravity do its thing.
PRACTICING: Building up to do a bunnyhop of more than 2 inches is NOT something that will happen over night. It can take months to learn to bunnyhop up a curb. It can take YEARS to learn to bunnyhop a couple of feet high. Practice about 3 to 5 minutes a day EVERY day to get better at it.
FACTORS: Since bunnyhopping involves a lot of physics stuff you need to consider the following- Bike length, bike weight, YOUR weight, how high YOU can jump, and how strong you are. These will ALL affect how high you are able to get the bike. Remember if you are small and have a heavy bike you will NOT be able to learn as quickly to go high.
HINTS: Ride towards a curb (a 5 inch or so curb) at a VERY slow speed. Lift your front wheel onto the curb and then lift your rear wheel onto the curb. Do not put your foot down. Do not let either tire hit the curb.
When you can do this with neither tire hitting the curb... go faster and learn the motion of lifting the front tire first then the rear tire. This rocking motion is what makes a HIGH bunnyhop possible. At some point you should be travelling at the curb fast enough to lift the front wheel onto it and then the back wheel onto it BEFORE the front wheel lands. THIS is a bunnyhop.
LIFTING THE BIKE: Possibly the number one reason people can't do bunnyhops to begin with is that they don't understand the concept of locking their feet against the pedals. There is a reason that pedals (especially aluminum ones) have those little studs on them. If you look at the video you will see how it is possible to lock your feet against the pedals and just lift the back end of the bike off the ground. This is the same action that snaps the back end into the air when the front wheel is off of the ground. It is also a good way to help to learn the trick."