It will depend on a number of factors. Firstly the legal requirements set down by the airlines licensing agency (FAA, CAA etc). Secondly its comes down to the airlines own policy. An S/O in some airlines is merely a cruise relief pilot. They are trained only to operate when above certain FL's and do things like monitor the fuel, do the plog, liaise with ATC, request step climbs etc. Having them on board enables the crew to fly for longer and it reduces costs. They won't get to land or take off. Its worth noting that in the "old days" many skippers would let the better S/O's have a go at landing but for most airlines those days are long gone and everything is by the book. The closest they might get to landing is in the sim to cover for the rare occasion of a multiple incapacitation.
Some S/O's are fully type rated, some do abridged courses and only receive a full type rating when made up to F/O. Really depends who you are looking at.