What is the procedure for going from discovery board to a deployable solution?
You first make a list of the components that you have used on the discovery board and how they are attached to the microcontroller - i.e. power supply, LCD, buttons, LEDs, I/O ports. Then you design a custom board that replicates the functionality of the stuff on your list and attaches the components to the controller in the same way. And you leave out stuff you didn't use, of course - if your discovery board has an SD card slot, for example, and your design doesn't use it, you don't need to put an SD card slot on your production board.

As a hobbyist, you do exactly the same as a business. Getting a PCB manufactured isn't that expensive anymore. (It might be more expensive than a bunch of discovery boards, however, depending on how many you need.)

TL;DR: Develop on the discovery board that has all the features / components you could possibly need, then trim it down to only the stuff you really need on your production board.