Removing a champagne cork is a very simple process when approached with a basic level of common sense.
There are a few layers to get through before actually getting to the cork of a sparkling wine bottle. First, remove enough foil from the top of the bottle to reveal the cork, the cork is covered by a wire cage, on the side of the wire cage you will see a section of wire twisted into a little handle. Pull that handle away from the side of the cage and untwist the wire, please be careful as you do this being sure to point the bottle away from yourself and any other people in the room! There is a reason that the wire is there, the champagne cork could release at any moment… at really high speeds thus causing injury or perhaps breaking a window or light fixture.
[Here is a way to amuse your friends and family - most, if not all wire cage handles are twisted with exactly 6 half turns... you can amaze and thrill everyone with this bit of knowledge]
Once the cage has been removed, continue to keep a firm hold of the bottle while gripping the cork with the other hand. Slowly twist the bottle round (not the cork), remember the goal here is for the cork to emerge from the bottle with a small sigh and not a loud explosion, after all, the louder the pop, the fewer bubbles you will enjoy later.
There are many good devices that can be used to help in opening sparkling wine, here are a few good examples: