The most important thing in opening a bottle of Champagne is to accomplish the task with such aplomb that it will appear to your guests as if you do it every day.
This is very difficult to pull off while wincing at the expectation of imminent disaster. So conquer your fears by practicing a couple of times alone with some cheap sparkling wine as follows.
First, remove the foil wrap covering the wire muzzle and the cork. To help you do that neatly without tearing all the foil away from the neck of the bottle, there is often a small tab to pull. (In my experience, either I can’t find it or it tears off when I pull it.)
With one hand, grasp the bottle firmly around its neck while pressing your thumb down on the top of the cork as insurance against the embarrassment of a premature evacuation. With your other hand, untwist the wire loop at the base of the muzzle and remove the wire.
Now move your bottle holding hand down to the bottle’s widest part and tilt it away from you at a 45º angle. (More about that later.) With your free hand, grip the cork firmly and twist the bottle, not the cork, until the cork begins to loosen, and then continue more slowly until the cork eases out. If you are faced with a recalcitrant cork that refuses to move, rock the cork with a forward-backward motion to loosen the stickiness between the glass and the cork.
Now, why did I say that you should twist the bottle, not the cork? Both Newton and Einstein agree that it shouldn’t matter at all which one you twist, because the motion is strictly relative.
You could slice a loaf of bread by rubbing the loaf against the knife, couldn’t you? But think about it: In twisting out a cork, you must reposition your fingers several times, temporarily relinquishing your grip on it. During one of those times, it could pop out uncontrollably, depositing wine on the floor and egg on your face.
About tilting the bottle: You don’t want it to be vertical, of course, because you’d be in danger of shooting yourself in the face if the cork popped out. On the other hand, if the bottle is too close to horizontal the neck gets filled with liquid and the “head-space” gas floats up to form a bubble in the bottle’s shoulder.
Then, when you release the pressure by removing the cork, the bubble expands suddenly, expelling the liquid in the neck. A 45º tilt will usually ensure that the head-space gas stays up in the neck, where it belongs.