Untwist and remove the wire cage around the cork, keeping your thumb on top in case the pressure alone is strong enough to push the cork out.
Carefully place a cloth napkin over the cork, so if the cork pops it will go into the napkin, avoiding any injuries.
Slowly twist the bottle, not the cap, until you stop hearing a fizz, and then remove it completely. Although it may seem dramatic to let the cork "pop", it results in carbon dioxide loss, which is what gives champagne its sparkle.
Gently pour the champagne down the side of a glass and enjoy!