A Champagne bottle holds a considerable amount of pressure. Early bottle designs used to explode and the manufacturers kept making them thicker until they could contain the pressure that is caused by the release of carbon dioxide during the fermentation.
At the opening of the bottle there is a lip that creates a stress concentration. On the vertical seam of the bottle the glass is not as uniform, which creates a second stress concentration - it is this intersection of the seam and the lip where the bottle will be significantly weaker is the best place to strike with the sabrage sword.
The impact of the sabre on this weak point creates a crack that rapidly propagates through the glass. Combined with the momentum of the sabre and the pressure in the bottle the crack will grow. Once the crack has severed the top from the bottle, the pressure inside the bottle and the transferred momentum from the sabre will send the top flying, typically for a distance of five to ten metres.
The trick is to hit the bottle with a clean, smooth and above all "confident" stroke. If right handed hold the bottle in your left hand at arms length with thumb in the bottle depression and hold firmly. Hold the bottle at about 45-60 degrees to the horizontal. With the sabre in your right hand draw it back over your left shoulder and aim to stike the weak point as described above. Strike the bottle quickly and smoothly and (like golf) ensure a good follow through above your head. You should always use the blunt edge of the sabre and not the sharper leading edge.
Andrew Coghlan displays the follow through action of the sabrage sword. Note the distance of the cork (circled) before any Champagne has started to flow from the bottle.