The key is to remember that O2 is the terminal electron acceptor in the electron transport system. As long as there is O2 and glucose available, you can keep burning glucose and making ATP. While that's happening you are in an aerobic state. So you're incorrect in that while sitting down you are in an aerobic state.
Now, when your body is under exertion, you may not be able to get enough O2 into your cells to oxidize all that NADH you're making to make all the ATP that you need. Then the whole electron transport system and citric acid cycle gets backed up and pyruvate and NADH start accumulating in the cell. If this condition persists, glycolysis will get backed up as well and then you're really stuck (Remember, GAPDH in glycolysis requires NAD+). You need a way to get rid of the pyruvate and oxidize the NADH back to NAD+ so that glycolysis can continue. Remember glycolysis has a net yield of 2 ATP all by itself. This is enough to keep you going for a while, so that basic cellular functions don't shut down.
The answer is to ferment. There are basically two types of fermentation that you should know about:
1. lactic acid fermentation. In this mechanism the pyruvate gets reduced by the NADH, forming lactate. Thus, pyruvate levels decrease and NAD+ is regenerated. Only problem is that the lactate will start to accumulate after a while, and that's not good either. If you're a small organism, it's no problem because the lactate can just diffuse away. Many small organisms rely on this type of metabolism exclusively and don't use the oxidative pathway at all. But if it's happening in your muscles, the lactate basically just hangs out until oxygen can be restored, whereupon the reaction reverses and all those extra electrons can drain into the oxidative pathway. In a vertebrate most that lactate actually gets transported through the bloodstream to the liver where it is converted back into glucose.
2. alcoholic fermentation. In this system the pyruvate is decarboxylated to acetaldehyde + CO2, and the acetaldehyde is then reduced by NADH to form ethanol and NAD+. This is what yeast do; we take advantage of the CO2 to make our bread rise and the ethanol to make our booze. ;)