A common misconception is that leaning a motorcycle is what causes it to turn, and the more you lean the faster it will turn. One of the teachers made a bike with fixed handlebars and turning forks (maybe Keith Code), to show students that all the leaning in the world would not turn this bike very well.
You turn the handlebars with countersteering if you are going more than about 2 mph, which comes naturally if you rode a bicycle first, and the more you turn (push) the handlebars and the faster you are going, the more the bike will lean afterwards. If you are going way too fast and turning (pushing) the handlebars way too sharp, the scraping metal parts (hopefully a footpeg feeler- on my old bike the exhaust pipe scraped first on the right side) will start to lift the back tire off the ground or cause the front tire to start to slide (tuck). If this happens, do not panic- suddenly putting the throttle to idle, pulling in the clutch all the way, or slamming on one or both brakes usually causes more problems.