The first question most people ask when introduced to the golf swing plane is "what is it?" Well, before we get into the mechanics let me just say that if understood and the techniques I mention below are applied, the swing plane will help improve a golfers game no end!
Golfing idol Ben Hogan was one of the biggest advocates of maintaining a controlled swing plane and for good reason as his shot consistency improved and he went on to become one of the best hitters on the PGA tour.
Imagine that your swing is a pendulum. Ideally, you want your club head to follow the arc of a pendulum when you take your club back, through your downswing, on impact, and on your follow through. That is your swing plane. If it's offline to the left or right, you're going to be hooking or slicing.
If you're off your swing plane, you will be making constant adjustments during your swing - whether you know it or not. These could be subtle and not-so-subtle movements made so you hit the ball squarely. Too far outside? You will pull in your arms or straighten your stance. Too far inside? You may have to lean forward slightly to try to make contact. All of these corrections are damaging because they take focus and power away from your shot. Mastering a great swing plane is the result of mastering the proper swing fundamentals.
Firstly, you must master your stance. You should be bent forward at the hips and not hunched at the shoulders with your back flat and your knees slightly bent. Keeping your back flat will stop you swinging with your arms (big mistake) and will enable your back to act as the axis. Turning your shoulders as you take a backswing will create the torque and bringing your club down will release the torque at the waist, with your arms merely guiding the club.
Make sure you also don't swing your hips and body backwards during your back swing - this is a very common mistake and will take the club head off-plane and most likely result in a slice. Focus on keeping your hips still and twist at your wait during your backswing. Don't move your hips forward either as this will have the opposite effect and result in a hook.
Here's a final tip to help you maintain your swing plane. Take two wooden sticks or broken clubs and stick them in the ground about 3 inches from each hip. Practice your shots and concentrate on not touching the sticks. If you can master this, you're beginning to master your swing plane!