Century has most of the docs on their website for their products. Be careful about models because the III may not be the same as the IIIc.
If you're looking at a IIIc I can fill in some details. If you're looking at a III, I believe Ted's Aztruck has one. They are different critters...
AFaIK Ted's autopilot was a Piper Autocontrol IIIb which is quite a bit different than a Century III although I do believe it was made by Edo-Aire which became Century at some point.
Despite it's age, the Century III is a fairly capable unit. Fully optioned with a HSI, a radio coupler, and a glideslope coupler it can track a VOR or GPS course, hold a heading, intercept a course (from a fixed 45° angle), hold pitch, hold altitude, and capture/follow a glideslope (ILS or LPV). The roll control functions (heading, tracking, etc) can be activated without the pitch axis, something that many newer autopilots don't allow. It does lack several features found in more modern units such as altitude pre-select, constant vertical speed climbs and descents, all angle intercept, CWS, go-around, and there's no flight director option. There is no microprocessor, built in self test or fancy annunciator panel either.
If you add GPSS driven by some WAAS GPS navigators you gain the ability for hands off autopilot flown course changes (bends), DME arcs, procedure turns, and holds. That combination can track an entire approach complete with the missed portion terminated in a hold with almost no input from the pilot other than power and configuration changes (you do have to manage the pitch axis on the miss).
If the electronics are healthy and the servos are in decent shape (they typically need their motors cleaned up every 1000 hours of operation).
It relies on pitch and roll feedback from an air powered attitude indicator so if you lose vacuum you lose the autopilot as well. Almost all Century IIIs were installed with manual/auto electric trim
There are some potential maintenance issues: The Century III is a very old design and the earliest versions were plagued with problems due to a circuit board fabrication method that used "griplets" instead of plated thru-holes for connections. If your autopilot has any of those, you can pretty much guarantee you will need to replace them. Fortunately used circuit boards with a better design can usually be found at a reasonable price.
Century also used a connector style in their wiring harness which tends to develop poor connections over time. There is a newer version of the same connector which can be used for replacement but it would be a fair amount of effort to replace every one. I have successfully resolved a few connector problems by "tweaking" the female socket pins with a dental pick and so far haven't had to replace more than one connector.