There are essentially two types of sparkling wine; bottle fermented and tank method, where both start with a base white wine. This white wine is made as described on the Vegan White Wine page, and can therefore be vegan or not depending on the finings used (if any).
Very cheap ‘sparkling wine’ can literally be white wine that has been artificially carbonated. Truly a case of you get what you pay for, so do expect to pay more for a sparkling wine than a still wine as it has been through an additional process.
Bottle fermented wines include Champagne, Crémant, Méthode Cap Classique and Cava.
To create a bottle fermented wine, the white base wine is mixed with sugar and yeast, and then sealed into the bottle. At which point, the wine goes through a second fermentation. This process increases the alcohol slightly and also produces carbon dioxide. Because the bottle is sealed (and the gas cannot escape), this carbon dioxide dissolves into the wine making it naturally sparkling. Additionally, this second fermentation forms a sediment of dead yeast cells (the lees), which release the classic bready/biscuity flavours back into the wine during ageing. After the wine is aged, the yeasty deposit is removed to leave a clear wine.
Tank method wines typically include Prosecco and Asti. They are less labour intensive than bottle fermented wines and are therefore often cheaper.
To create a tank method wine, the white base wine is put into a pressurised tank along with sugar and yeast, and then sealed. Again the wine goes through a second fermentation, which increases the alcohol slightly and creates a natural sparkle from dissolved carbon dioxide. After fermentation, the wine is filtered and bottled (meaning no sediment is left giving little or no bready/biscuity flavours). As a result, tank method wines are usually in a fresher, fruitier style.