Actually this is incorrect at speed. Once above about 7-10mph (depends on bikes but applies to motorcycles too) you actually push the handlebars on the side you want to turn. In other words, push right to turn right, push left to go left. Only at walking pace or what would be pretty low speeds do you actually turn the handlebars in the direction of the turn. The harder you push the quicker the bike will lean over and turn harder. It is more obvious on a motorcycle at higher speeds but it is there on bikes and motorcycles one you get above a fast job. So push left, go left; push right, go right. Don't be too agressive when trying this for the first time and at speed. You can snap your bike over quite quickly this way.