Unless you're making a drink where the flavor of the Champagne really matters (like the Classic Champagne Cocktail), generally, inexpensive alternatives such as Cava, Sekt, Prosecco or California sparkling wine work well.
Always pour the mixers in first, then top off with Champagne to avoid fizzy overflow.
This one's a brunch classic. Increase the flavor by using a 1:5 ratio of freshly-squeezed orange juice to Champagne. Then add a splash of triple sec.
The fancy cousin to the made-with-white-wine Kir, the Kir Royale consists of a dash of creme de cassis (currant syrup), topped off with Champagne.
Invented at Harry's Bar in Venice, the Bellini is best when made with ripe peaches. If peaches aren't in season, try creme de peche (peach syrup). Use a 1:4 ratio of syrup to prosecco.
This is an easy and strangely delicious drink with a 4:1 ratio of Champagne to black Irish stout.
Death in the Afternoon
Traditionally made from absinthe, a spirit now illegal in the United States, in a 0.5:5 ratio to Champagne, you can probably substitute pastis or another anise-flavored liqueur.
For a holiday brunch, make Poinsettias: a 1:4 ratio of triple sec to Champagne, with a splash of cranberry juice added for color.
Named for the British Admiral George Nelson, this makes a great, if slightly morbid-sounding, party drink. The recipe calls for a 5:1 ratio of Champagne to tawny Port.
Moving on to the slightly more complicated ones...
Classic Champagne Cocktail
Soak a sugar cube in bitters, drop it into a flute, fill the flute with Champagne and garnish with a twist of lemon. This classic drink dates back to at least the mid-19th century.
There are a number of French 75 recipes floating around; the only thing people agree on is that it's a serious drink with serious ramifications. Here's the classic: a splash of simple syrup, a bigger splash of lemon juice, an even bigger splash (about an ounce) of gin, topped off with a glassful of Champagne.