For Champagne it is quite a process, wines are fermented from three types of grapes (pinot noir, pinot meunier, and chardonnay/ 2 reds and a white grape varietal) these wines then are blended from different vintages, and in different proportions. This is then put into champagne bottles with yeast and sugar, where it will rest at a 45 degree angle where they will be riddled (quick jerk shaking action) every one to three days. After the aging time on it lees (the sugar and yeast mix) the bottle will be disgorged (the lees will be removed) through a process where the neck is slightly frozen. Upon opening the yeast will shoot out, and then the bottles will be topped off with a blend of still wines. After this point they are corked and set to age in the caves.
Really quick overview, but gives you the jist of it. You can do the same with beer too, with equally enjoyable results.