I have made champagne several different ways...
1) Take still wine that has been aged. Be carefule to keep the SO level low. Prime wine with 24 grams of sugar and create a Dosage (mixture of sugar and yeast) and add to bottle. Pour primed wine over the dosage, cap, and age the bottle on its side.
2) Take wine that is nearly completed fermentation. The sugar level should be near 0, but the wine should still be very cloudy with still active yeast. Pour 24 grams of priming sugar into each champagne bottle and pour active wine over it. Cap and age bottle laying on its side.
3) Much like method 1, except I place the dosage into a packet of micro pourus tubing (they make this stuff for kidney diallisys). This is tubing that "traps" the yeast making disgorging a snap.
4) Much like method 2, except I place the champagne into a Korny keg (5 gallon SS keg) and seal it.
Out of all 4 methods, Using the keg is best. The keg draws off the bottom, so when you first start pouring, you get the sediment on the bottom, then nice clear champagne.
If I just wanted to go bottle by bottle, I use method 2. I have found that I have real problems getting the fermentation to kick back off once the wine has gone still. Capping while you have active yeast will almost gaurentee success.