There are two processes that wine undergoes while oxidising, the first and most important is oxidation and the second is the conversion of alcohol
(ethanol) into acetic acid or vinegar.
When wine is exposed to the air, Oxygen in the air interacts with the wine. The wine changes colour and turns both white and red wines brown.
Flavour molecules absorb the oxygen changing the flavours in the wine. A small amount opens up the fruit flavours, decreases tannins and acidity and generally enhances the wine. This is known as letting the wine breath. Too much oxygen and the fruit flavours are destroyed, and the wine can lose both acidity and or tannins. The rate of chemical change is dependent on how much oxygen the wine is exposed to, the pH of the wine and any preservatives in the wine.
Wine naturally has ways of controlling oxygen. Red wines have high levels of polyphenols that can absorb oxygen. For example tannins are a type of polyphenol and absorb oxygen, so does anthocyanin a group of chemicals that give wine it's colour. As red wines have more tannins and colour compared to whites, they are also more stable than white. Luckily for white wines which often have high levels of acidity, the speed that oxidation occurs is governed by the pH. The lower the pH (i.e. higheracidity) the slower the oxidation occurs.
In addition to the natural protection wines have, sulphur dioxide is added to wine. Sulphur dioxide prevents oxidation by binding with the precursors involved in oxidative reactions preventing them from reacting with oxygen or by binding with compounds already oxidized to reverse oxygen’s effect.
So wines with high acidity oxidise slower. Tannic and deeply coloured red wines also react slower. So a tannic and highly acidic wine will oxidise slower than a wine with lower acidity.
The second effect of oxygen is the wine tasting like vinegar. This is done by fermentation of ethanol into acetic acid by a bacteria called Acetobacter. Acetobacteris common in the air and wine exposed to the air will be effected by it eventually. However it can be managed by moderate levels of sulphur dioxide in the wine. So wines with sulphur dioxide are unlikely to turn to vinegar until the wine has been exposed to the air for some time and most of the preserving sulphur dioxide has been bound up by the wine. Turning wine into vinegar is a two step process with the Acetobacter bacteria first converting ethanol to acetaldehyde, which is often said to smell of bruised apples. The acetaldehyde then oxidises to Acetic acid and will start to smell like vinegar.
My personal experience is that the wine loses its fresh fruit smell both in intensity and definition within one to 5 days. It will then develop a bruised apple smell, sometimes I think it can smell more like red apples than bruised. But it takes a failure of a cork or abandonment of a wine for weeks before any vinegar smell starts to appear. That is not to say it doesn’t happen but the time taken for the reaction to occur is slow and is unlikely to occur from opening a bottle and waiting a week before drinking. You may come across an aged wine that has had a cork fail and has had years to turn to vinegar, but once again I have not come across this myself. That said, I have met a few bottles that were like a very rusty nail in colour, and unpleasant to taste, just not vinegar.
If deliberately exposed during winemaking, the wine may develop a range of aromas, however it is likely to also lose some of its primary fruit aromas. Examples of deliberate oxidation exist for some styles of Chardonnay, Oloroso Sherry, Tawny Ports and Madeira.