The making of air coolers starts with the design of the equipment required to perform the process of heat removal from the process fluid. There is a number of reputable software performing the mentioned heat transfer design (HTRI, etc). Then you could start with the mechanical design of the cooler, based on the selected / approved code ( ASME, EN, etc).
The mechanical design codes will guide you in the secrets of fabrication, inspection, testing of the equipment, including references to many related standards.
Basically, if you have a complete mechanical design, ie set of fabrication drawings, you can ask the people in the workshop how they make every component, including assembly until finished cooler is ready for delivery.
I believe that the process of learning step by step the process of making those exchangers would take a few years, if you want to understand that process.
Hope it helps,
Cheers,
gr2vessels

To supplement gr2vessels post, get out on the manufacturing floor if/when you can and take a look at the process.  Perhaps there are some "established" model offerings in addition to specialized models.  Let your curiosity guide you.

Regards,