It's quite concerning how many airline captains struggle to produce a load plan and load sheet for their aircraft
In Europe at least, most loadsheets are either produced by the dispatcher (who is weight and balanced trained) or via Centralised Load Control (CLC). Most airlines opt for CLC with the exception of people like Easyjet/Air Berlin who use a 'less paper cockpit' environment to produce the loadsheet, it's done by entering pax numbers / fuel figs / bag figs into a computer, information is passed to them by the dispatcher.
You can also do a manual loadsheet for any aircraft but this tends to be quite rare, other than small props and the like. Ryanair dispatchers produce a manual loadsheet for their flights but it's different than a 'drop line' one and fairly simple once you know what you're doing, some very clever mathematics are involved.
So in short, the captain/fo SHOULD be able to produce a load plan and load sheet but in reality they rarely do, and would probably struggle to produce a manual load sheet for lets say a wide bodied TATL flight.