What is FTP?

By definition, FTP is the amount of power (Watts) a cyclist can put out over one hour. This makes testing it quite difficult. To do it properly not only requires one hour of your time, on a bike, at maximum sustainable effort level - but for non-Time Trial types it requires a lot of learning about how hard can you go for one hour in the first place.
As a result of this, there are a lot of short-cut methods to estimate FTP.
Most of them involve some sort of 20 minute test and then reducing the power measured by a small percentage to estimate FTP. My favourite one is using the Xert app on my Garmin that employs a complicated algorithm and your regular riding to accurately estimate FTP - if done in a race situation where you are riding hardest at the end of the race the purveyors of the app (and my testing) suggest that it can be within a few Watts of actual value.
The final method I'll discuss is from The Sufferfest. Their 4DP (4-Dimensional Power) test protocol does require an hour of your time, but it isn't a traditional one-hour TT effort. Sufferfest tailors your exercises based on the four results of this test (Neuromuscular Power, Anaerobic Capacity, Maximal Aerobic Power and Functional Threshold Power). The FTP component is based on a 20-minute test, but one done after the NM and MAP tests are completed - so there is no conversion factor involved. They believe that one's 20-min ability after 3 shorter efforts is equal to one's 60-minute ability without these prior efforts (and finally one does the one-minute AC test that is completely brutal after all that came before).