Being able to unweight your rear wheel, or even 'bunny hop' your bike into the air is a damn handy trick for flying over gnarly terrain like rocks, water bars and greasy tree roots. You'll be able to travel faster, avoiding nasties like snake bites (compression punctures) and taco'd wheels, plus it looks dead cool.
The Zen principle behind this number is to make your handle bars accelerate faster than the front wheel. To get a feel for the sensation - leap off your mount, grab a fistful of front brake so the wheel locks up, and twist the handle bars forward, pushing the bike over its front wheel. The rear wheel will pop up like a slice of raisin toast. Then try it without using the brake - by gripping the handle bars tightly and rolling your wrists forward with an explosive action. Now try the real thing. Find a smooth, flat area and ride at a moderate speed in a straight line. Now ... 1. Grip your handle bars tightly, so your knuckles are white! 2. Get out of the saddle and move your weight forward until your head is well forward of the front axle. Your arms rather than your feet should now be supporting most of your body weight. 3. Twist the handle bars and push the bike forward with an explosive action (don't touch the brakes or you'll stack it big time). 4. Your legs should be relaxed, bent slightly to allow the bike to rise under you. The rear wheel will momentarily lift off the ground - a scary sensation but fear not... you're unlikely to head over heels. Thanks to Mr Newton, as you push the bike forward your body automatically moves back to return the rear wheel to terra firma.
Note that the differential between your handle bars and saddle should be 25-50mm. If your bars are too low, you will suffer from reduced leverage making the whole manoeuvre even harder. Once you've got this mastered, try combining it with a front wheel lift. This is the go for clearing drains, logs etc. at relatively slow speeds.
But when you've got the hammer down ,there's just no time to lift your front and rear wheels independently. You need to hoist the entire catastrophe into the air in a single movement. Intuitively people do this by yanking up on their pedals and handle bars. While this does work after a fashion, it's preferable to link the front and rear wheel lift together in a single fluid motion so you arc over the obstacle. Here's how... 1. Lift your butt off the seat and move your upper body forward and down over the handle bars. This compresses your body like a loaded spring, plus it compresses the front tyre and shocks. 2. Explode upwards or apply a 'power stroke' to bring the front wheel up. 3. Then as with the rear wheel lift above - twist the bike forward over the front wheel while it is still off the ground. This will cause the front wheel to lose some height. Remember to keep your legs relaxed, giving the bike room to float up under your body. 4. Extend your arms and legs to absorb the shock on landing - and hopefully you've already considered the drop zone in your pre-launch checks.
The bike will effectively out accelerate your body - starting behind you, and finishing ahead of you. You shouldn't need to pull up on your clip-less pedals - BMX and trial riders leap amazing heights with flat pedals. In fact it's advisable to master the bunny hop without your SPD's so you don't get tempted into bad habits. Practice is everything.