Natural wine is different as far as the wine making process is concerned, mainly because of it's exclusion of sulfur. Sulfur is used in the production of 99% of wine in the world today because it has a preservative effect. It protects the wine from the effects of oxygen and can kill off some nasty bacterias that live in the vineyard and threaten the flavor of wine. It's also used to kill off the wild yeasts living in the vineyard, so cultured yeast can be added in its place. A little sulfur is also used at bottling (even by quite a few natural winemakers) to help protect the wine during it's trip to where ever it's going.
Natural winemakers would rather take the risk of letting some of these bacterias in. That's because they prefer to use the wild yeasts, saying they add another essential element of terroir that makes each of their wines unique and different. I've also been told by a natural wine maker, who I consider quite extreme in his natural-ness, that I would be able to tell the difference in flavor if I tasted the same wine, one sulfured and bottling, and one not. I can't really say whether or not that's true, because I've never been able to carry out that experiment. But I can say the winemakers here in France that use zero sulfur make some of my most favorite natural wines.
So if most of the wine world thinks you have to have sulfur in there to keep the wine safe, how do the natural guys do it? The first and probably most popular technique in use today is Carbonic Maceration. Whether it was Jules Chauvet, or Jacques Néauport who made this method popular for natural winemaking, it doesn't really matter. In carbonic maceration, the winemaker tosses the whole bunches of grapes in the tank, rather than destemming and pressing them for their juice. The tank is sealed on top, and the grapes just sit there. The weight of the grapes starts to crush some of the grapes on the bottom, and fermentation starts naturally. The tank is sealed, so as carbon dioxide is produced, pressure is exerted on the remaining grapes, which pops any skins still not crushed. The resulting wine is usually quite fruity, light in tannins, and easy-drinking.
So, how does carbonic maceration help the winemaker avoid using sulfur? The answer is that the carbon dioxide gas released acts as an alternative protection against the evil forces of oxygen, by forming a protective blanket over the juice. The winemaker leaves the tank sealed until it's time to bottle, and then will usually let the gas escape right before putting it in the bottle. Sometimes they will even leave a little of the gas in the wine, to act as an additional preservative while the wine travels to its final destination. That's why sometimes you'll feel a little prickle for the first few sips of a natural wine.
Sounds simple, right? The thing is, as always with wine, it's not quite that simple. There are those winemakers who do strict carbonic maceration, but then there are also those who something called semi-carbonic maceration. These winemakers do the traditional fermentation I've described, but then they let the skins soak in the juice for a while longer to extract more tannin and structure, making a heavier, perhaps more serious, and age-worthy wine. They're still working under the cloud of protective gas, but then they're adding another layer of more traditional wine making on top, to make a very different style of wine.
And of course, it's not so simple as those two methods. There's really a whole continuum of people in between. Some will de-stem the bunches of grapes and then do a carbonic maceration style fermentation. And some will do a completely normal fermentation with a pressing, but then just leave the tank sealed to keep in the protective gas. So, for a wine professional who's trying to understand why a wine tastes a certain way, it can be pretty complicated. Basically, these winemakers do what they feel like and what they think will make the style they're looking for, with total disregard to all the established rules of winemaking you read about in books, and that's what makes it interesting. Basically you could say there are as many natural winemaking techniques as there are different natural winemakers. But what most of them do have in common is this use of carbon dioxide as an anti-oxidant, instead of sulfur.