Although you might be confused by the variety of "swings" taught by different instructors, they all teach a few common basics. No matter who teaches you the game, most teachers will include the same basic moves and positions. Once you know what these basics are, you'll have a much easier time understanding what makes each instructor's teaching different from the others. You'll also find that it's easier to keep your swing working properly.
You'll find slight differences in setup among instructors, but all of them will teach you a consistent posture that keeps you balanced throughout your swing. They'll tell you to flex your knees slightly and bend forward from the hips. This is a natural, athletic posture for most people; it should feel fairly comfortable. And if you do it right, your weight will feel like it's centered over the balls of your feet. From this position, you can turn from side to side while keeping your balance easily.
Not all instructors use the term "one-piece takeaway," but that's what a good shoulder coil is. You don't have to lock your elbows to keep your arms straight when you start your backswing; if you start it by turning your shoulders, your arms can stay relaxed and still stay relatively straight. If you coil enough that your arms are still straight when your hands reach the waist-high position, you've made most of the shoulder turn you need to create power in your swing.
Cock Your Wrists
Once you get coiled properly, your right elbow will start to bend (if you're a right-handed player). Bending that elbow is what causes your wrists to cock – if one arm stays long (straight) and the other shortens (bends), the wrists will have to cock. That wrist cock forms an "L" between your left forearm and the club shaft. It happens when your hands get around shoulder height. From there, your hands move very little to reach the top of the swing.
Unwind to the Finish
Unwinding your body so that you hit the ball and make a complete finish to your swing is a combination of two simple moves. To get through the ball, you can imagine a mirror image of the "L" you formed on the backswing. Just swing so it happens again at shoulder height on the other side of the ball. If you keep your grip relaxed, your wrists will uncock to hit the ball and re-cock on the finish without much help from you. And since your chest was turned away from the target at the top of your backswing, think about turning your chest so it faces the target when you finish. This will help you make a full downswing and finish in a balanced position.