Most riders can corner competently when they have only one bend to think about. But when corners come quickly, one after another as they might on a curvy country road or descent, you need rhythm and planning to stay smooth and in control.
Next time you're riding on a twisty road, work on these skills:
Take the first corner correctly. Relax your upper body. Put the outside pedal down (the right pedal for a left turn) as you begin coasting, and stand on it with all your weight. Slide your hips to the rear of the saddle and bend your arms to get low along the top tube. Help the bike lean into the corner by pulling up slightly with your outside hand.
Some riders like to point their inside knee into the turn, while others push it into the top tube, keeping their body upright as the bike leans over. Experiment to see which method feels right to you.
Anticipate the second corner. This is the key. It isn't the first corner that gets you, it's the next one -- and the one after that. The reason? Most riders know to enter corners wide, cut across the apex and exit wide so the corner is made as shallow as possible. But then you need to immediately set up for the next one. Plan your line at least one bend ahead.
Keep speed in reserve. This isn't a race! If you're leaning the bike way over and just barely making it around consecutive corners with tires chattering and your heart pounding, you're taking way too much risk. The goal is to smoothly slalom down a twisty road without needlessly sacrificing speed or safety.
Practice! Set several paper cups about 30 feet apart in a line, heading downhill in a slightly sloping empty parking lot. (Put water in them if it's windy.) Work on setting up each succeeding turn by using quick-but-smooth transitions.