Champagne, of course, doesn't require a corkscrew. But there is still a careful technique required to opening, which doesn't involve emulating the antics of a Formula One race-car winner and spraying it all over the crowd.
First - chill the Champagne down to 8-10°C for Vintage, Prestige Cuvée and 6-8°C for NV (non-vintage), Méthode Traditionnelle, Sparkling, Cava, Sekt, Prosecco and Asti.
Start with the bottle standing upright on a table or flat surface. Locate the wire loop beneath the foil capsule; by feeling around the neck of the bottle (some bottles have an easy peel tab on the side). Getting your thumbnail behind the loop, pull it out and downwards, tearing away the capsule as you do so. Proceed to remove the rest of the capsule / foil.

 

Grasp the neck of the bottle, keeping your thumb firmly over the top of the cork. This prevents it flying out with the potential to cause damage or even injury.
Then untwist the wire loop, and loosen the cage. Don't loosen your grip though!

In my experience it makes the whole process so much easier if you keep the wire-cage on the cork, as the cage fits nicely into the sides of the cork and gives your hand something to grip and hold onto. Now, never taking your thumb from its secure position over the top of the cork, pick up the bottle. Firmly grasp the cork and cage between thumb and forefinger, and with the other hand, twist the bottle. (Yes - twist the bottle, it is much easier to twist/ turn the bottle than it is the cork and you also don't loose your tight grip on the cork).

As the cork moves, control its release with your thumb. Continue twisting the bottle away from the cork. Its eventual release should be accompanied by a gentle sigh of escaping CO2 gas. A louder pop suggests that you haven't controlled the extraction of the cork adequately, but as long as there is no loss of wine then this doesn't really matter.
Failure to control the cork at all, resulting in a fountain of Champagne, may produce a laugh and cheer, but ultimately this is just an expensive mistake and loss of Champagne.