Rider form:
In real life (and in TT), where the CG of the rider is greatly affects how the bike handles. For the most part, the goal is to get the CG as far to the inside of the bike as possible. This lets you turn the same arc, with the bike more upright (more upright = more grip = more acceleration). This is great for long sweepers, as you can maximise cornering clearance (the amount you can lean before hard parts start scraping the ground).
This isnt so great for tight transitions (left-right-left, for example). It takes a long time to transition the wieght from side to side, and it also upsets the bike whenever you shift your wieght. This is where the 'neutral' style comes into play. Still decent cornering clearance, but much more stable rider, therefore faster leans.
A bike does not lean instantly, a car can turn instantly... The secret to riding a bike fast (IRL and in TT), is to flick it over as fast as possible. The faster you can get it turned, the less time you have to be at full lean, and the more time you can accellerate.
The 'push it under' style is a big no-no in real life, it uselessly sucks up all your cornering clearance. Normally, people 'push it under' when they are afraid of leaning with the bike.
There are exceptions, as in motard racing, where you need to flick the bike side to side VERY quickly. And scince the riders can keep the bike up with thier feet (and are skilled at sliding..), this works out ok.
hope that helps somewhat.