What do you need to know? An FSPO is a ship shape floating production vessel (often built from a converted oil tanker). The vessel is moored in place and connected to the subsea wellheads by flexible risers. Export is by shuttle tanker or ocassionaly by a conventional export pipeline. The vessel may be spread moored (in calm waters) or moored with a turret, allowing the vessel to weathervane, in harsher waters. Turrets may be external or internally mounted; internally mounted turrents are more expensive but can cope with higher sea states etc.
Process facilites can be anything from just a 3 phase separator train with gas to flare to full export spec process systems with full water and gas injection systems: a big (say 50m x 150m) FPSO has a lot of deck space!
FPSO are very flexible; they've been used in thousands of meters of water offshore Brazil to a few meters of water offshore Nigeria; they can cope with as few as 2 -3 wells to as many as 60 or so, and throughputs can vary from a couple of thousand bbl/d to hundreds of thousands bbl/d. Storage can also range from a few thousand barrels to over a million barrels- some of these things are huge!
FPSOs are popular, expecially on marginal or small fields as they are cheap (especially conversions of existing tankers). One obvious disadvantage is they use subsea trees, and another is the lack of drilling/ workover facilities (although there are proposals for FDPSO- FPSOs with drilling capabilites). It is even possible to hire them from people like Oceaneering or Bluewater (do a Google on these companies to find out more about leasing an FPSO).