Well ... the common size such as you buy from Factors is Spark plug thread.

The theory is .. At around Lambda1 (near the point of the theoretical stochiometric ratio - 14.7:1) the sensor (which ideally, should be as close to the burn as possible ... even in it ... that will come soon enough) becomes very sensitive to the oxygen content in the gases. The output signal follows the ratio of the burn almost instantaneously. The signal, by design may be a (+) one (for lean ratio) or (-) for rich. The ouput voltages vary by design .. Some (like the 4.6 Rover with GEMS) are 5v.
The sensor consists of a precious metal "foil" protected by a permeable porcelain cap .. Design varies slightly, but most are built with the same principles.
Also, design can denote the mumber of connections .. The first (in the Yank motors way back) was a single wire type. Earth is through the body .. This is improved by a separate earth (2-wire) then an internal heater element (3 and 4 wire) On the latest sensors, there are generally 2 earths, 1 heater, and a signal. The reason for heaters is to get the sensor heated up quickly helping emissions during warm-up. To add something else, many modern management systems allow the addition of extra oxygen during the warm-up, which gets the cat heated up quicker to working temp. To some extent, the 02 lambda signal is ignored or modified to help.
Most current Euro4 emission spec. cars will have a twin lambda system .. the front one basically works as described above, the rear (post-cat) monitors the output gases and picks up failures/problems. This will trigger an event in the management ECU.

That's most of it, I think!