What would the requirements be to be able to take a non-EU spouse to Germany by a UK Citizen? Moving from a non-EU country into Germany? Does the non-EU need a visa, or can they work upon arrival with the EU spouse?
Formally, there are no requirements but only formalities. What this means is that an EU citizen's spouse has a very strong right to join the EU citizen living in another EU country and to work there. The host country may not apply its usual requirements (which, depending on the country might include things like language tests, diploma requirements, salary test, job market evaluation, etc.) and should merely check whether the person is indeed the spouse of an EU citizen residing in the country.
In practice, the non-EU citizen might still need a visa to enter Germany (depending on citizenship) and will certainly need a residence title (Aufenthaltstitel) to stay there for more than three months. Legally, the visas and residence permits only recognize and document this pre-existing right and should be issued quickly and free of charge. I suspect it would however be difficult to convince anybody to hire a non-EU citizen before you get the actual permit.
As far as I know, Germany follows EU law reasonably well in this respect so I would not expect unreasonable delays. I also think it's possible to enter Germany (with or without visa, depending on citizenship) and then to apply for the EU relatives residence permit from within the country (which is not always possible for other types of residence permits) but it might be best to check that with the German authorities in advance.
The place you will need to contact once you are in Germany is called the Ausländerbehörde or Ausländeramt. There is one per district (Landkreis) and in larger cities.