Q:

How were fighter jets built in the 1950's?

As far as I know, jets did not see mass production across the world until the 1950's. So I'm interested in how they were built in that time. How many different types of factories were needed? How did those factories work? What supplies were needed and how much manpower did they need per jet?
Right now I'm only imagining two kinds, an airframe factory and an engine factory. I'm very interested in learning more and would not be surprised if there are many other types of factories that go into making a fighter jet.
For simplicity, let's exclude electronics factories like the radar, and weapons factories like guns, bullets, and missiles.

A:

Building an airframe did not change all that much in the jet age. Assuming you are talking about all aluminum aircraft the power plant is somewhat abstracted from the equation in terms of a production line. 
Here is the assembly line that Lockheed had for the early P-80 Jets (not all that different than their propellor counter parts). This picture would make it seem as though the airframe was all built in one place as you can see it in various stages in this image alone.  

(source)
This is a pretty interesting article about the history of the plane and the role Kelly Johnson played in it. 
Like anything in the world of production the assembly line does not change nearly as much as the tooling does. One of main costs in bringing anything to production is cutting and preparing the tooling. Assembling a jet airframe was not all to different than assembling a high performance prop plane of the era. 
Things got more complex as they moved to more complicated materials (this came a bit later than your question references but none the less). By all accounts an enormous portion of the SR-71 Blackbird budget was spent developing tooling that could work with titanium. 
The engine companies (Like GE/P&W etc) saw much bigger changes as they were now making and testing a completely different product. The P-80 above housed a GE/Allison J33. This would have fallen on to GE to build and like many engines prior would have simply been bought by Lockheed for the plane. 
I will try and find some hard production numbers/times for this era of planes. 

