How do I learn about design for manufacturing?

Grab a copy of THE reference book Machinery’s Handbook. If you do anything with mechanical engineering or metalworking, Machinery’s Handbook is about as close to holy scripture as you can get in the industry. You may think you know a lot, but there are things in there that I never would’ve guessed even after a few years as a machinist.

I work at a UK University.

Here are the 5 texts recommended for first year Mech Eng students
Engineering Design Methods: Strategies for Product Design Cross, Nigel
Engineering Mathematics Through Applications Singh, Kuldeep
Introduction to Mechanical Engineering, An: Part 1 Clifford, Michael;Simmons, Kathy;Shipway, Philip
Principles of Modern Manufacturing Groover, Mikell P.
Thermodynamic and Transport Properties of Fluids: S. I. Units Rogers, G. F. C.;Mayhew, Y. R.

If you are more interested in design, we also teach Product Design. Here are the 4 recommended texts for that course
Manufacturing Processes for Design Professionals Thompson, Rob
Research Methods for Product Design Milton, Alex;Rodgers, Paul
Drawing ideas: A hand-drawn approach for better design Baskinger, Mark; Bardel, William
Prototyping and Modelmaking for Product Design Hallgrimsson, Bjarki

Hmm … you’ve probably got some good general references above, but my own suggestion would be to narrow your focus.

What kind of manufacturing? Mass produced consumer products? Industrial machinery and welded fabrication? Automotive parts? Furniture? Clothing? Pharmaceuticals? We manufacture so much and in such variety that you need to focus on the type of manufacturing that you want to learn about.

There is a TV series on Netflix and Cable called “How It’s Made”. Watch a few of them to get an overall understanding of manufacturing techniques and processes. The sow covers a wide variety of products spending about 5–10 minutes on each factory. In one show you can learn about the production of steel, toilet paper, and food condiments.
Excellent show.
How It’s Made on Discovery Science Channel