Although it varies by brand and type, dry wine contains very minimal amounts of sugar per glass, medium wine contains anywhere from .5 to 2 grams of sugar per 5 fluid ounce glass, and sweet wine can contain up to 6 or more grams of sugar per glass. Red wine typically has a higher sugar content than white wine.
The natural sugars in grapes are what turn into alcohol through the fermentation process of wine. Once fermented, the amount of residual sugar left in the wine determines the "dryness" of the wine. Dry wines contain the least amount of sugar while sweet, fruity wines contain much more sugar. Wine whose grapes are grown in warm regions tend to have more sugar than those whose grapes are grown in cooler regions.