Sparkling wine is generally made from less ripe grapes, resulting in higher acid and lower sugars. That said, there are a few places around the world that make a sparkling with ripe grapes.
Sparkling is very difficult to do well. One must make a base wine with quite a bit of acidity, this wine is then bottled with a calculated amount of sugar and yeast topped with a crown cap and aged generally for 1-3 years.
The bottles are then riddled for a week or two (Done on a mechanised rack almost across the industry) the neck of the bottle is then frozen. The crown cap is opened, the yeast are ejected, the wine is quickly topped, sugar is possibly added if desired, the wine is corked and caged, and will rest for another few months before release.
All this is pretty inaccessible, and dangerous, for the home winemaker. However a Petilant sparkling is within possibility. One would just skip the disgorging step after the secondary fermentation and make sure to decant the bottle on account of the slug of lees resting on the bottom.