a really easy way to understand how your bike steers is to do this (at relatively low speed to start with..)
on an open empty road at about 60k, take your hands off the bars... the bike will usually steer slightly one way or the other, try to correct it by 'leaning' hard to do! now try just pushing the bar (lightly, with your finger tip!) on the opposite side to the way the bike is steering itself.. instant straighten up with very little pressure. now push left or right and note the way the bike leans opposite and turns... try it the other way... this is how you steer your bike even if you don't think you are, but now that you know how to steer it, it becomes much easier and quicker to control in any situation.. when you are really confident about what you are doing, try pushing it around a few corners using the 'push the bars' method and see how easy it is to corner hard
how does it work? my understanding (might be wrong mind you!) is that when the front wheel is turned to the left by you pushing the right hand bar, the bike 'falls' away from the left (centrifugal force?) so leans to the right, when it leans, it turns...