I have noticed that one of the most frequently asked questions by new and old brewers is, is my beer done fermenting? Well, there are a few ways to answer that; varying from pitching more yeast to be sure, comparing the expected attenuation from the yeast manufacturer with the actual attenuation, or moving the beer to a warmer spot. I have never been a huge fan of any of these options because of loss of flavor from overpitching or the creation of esters from warming the whole batch.

The fast or forced fermentation test is a way to circumvent that process to analytically determine what you final gravity should be. The way that I like to go about this is to create a starter that is slightly larger than is needed, and to save about 8oz or so of unfermented wort. I then take a hydrometer reading (or brix), aerate, and then use the extra yeast to overpitch this small batch, and allow it to ferment in a slightly warmer area. You can also aerate this small batch throughout its fermentation because there is no worry about oxidation. After a few days the fermentation will be done and you can take a final gravity reading. This final gravity reading is what you would expect out of your larger batch based the yeast strain, particular batch, and optimal conditions for your yeast.
As a side note, you can also use a variation of this after fermentation has seemingly ended, but you are unsure if it is fully attenuated. All you need to do is take an aseptic sample from you wort, large enough for a hydrometer reading, and place it into a santized beer bottle with an airlock. I then place that sample (which was likely aerated from the transfer) in a warmer area and then check its reading about two days later. By doing this, you can tell whether your brew is finished fermenting.

P.S. This method is also useful in finding the expected attenuation of harvested yeast strains.