After reading paranoidfish's writeup, I realized that there were some key points he left out.
His technique, while suitable for mountain bikers and commuters, and substantially easier to perfect, will not yield the maximum height.
On a BMX bike, the position of the rider relative to the rest of the bike allows him/her to raise the front wheel a good distance from the ground while maintaining a comfortable balance with a minimum of effort, simply by pulling up on the handlebars and leaning back while kicking the pedals, and thus the rear end of the bike forward.
Holding that position, and riding in a
manual, is a tricky art that
requires practice, and involves a great deal of balance and a
quick finger on the brake lever. However,
from this position it is possible to
spring forward using the technique paranoidfish has already described, then
pull the back end up to achieve a maximum height. This should obviously be done
at speed, otherwise the bike will
fly out from under you.
The trick is to raise the front, then push off, then raise the back. I've seen
riders much more skilled than myself clear benches,
shopping carts, and
human debris this way. (It's surprising how a
small child who has wandered into the path immediately off the landing of a
large double after being brought to the
trails by his
idiot parents will scream when a
grown man on a child's bike jumps over them to avoid a
head-on collision)
Note that when jumping more than a foot or so off the ground, it is generally advisable to push the rear wheel down again, to avoid landing in an endo and flying over the handlebars. Like an airplane, a bicycle should take off, and more importantly, land rear-wheel first, or as close as possible.