Even the following motorcycle was having trouble keeping up. Climbers who win mountain climbs are often given the most attention, but just as much skill is required to descend - if not more, given that life is literally hanging in the balance as riders rocket down steep and twisting roads. To lean the bike, counter-steer by gently applying pressure on the handlebar toward the turn. This pushes the front wheel in the opposite direction from the turn, but allows you to lean into the turn with your bike. Turning the front wheel the opposite direction isn't intuitive, so practice on a quiet corner.
Balance is the second part of turning.
Keep your inside foot high up and away from the ground, at 12 o'clock, with knee bent and pointing toward the turn. Sit firmly on the saddle and ride with hands in the drops, fingers ready on the brake levers. Focus on pushing down hard on the outer pedal, which will naturally keep your weight balanced over the bicycle. The lower the lean, the faster the turn, but watch carefully for road conditions - wet roads, gravel and sand should factor in how far over you lean. Direction is the final point.