If I were to build a plane of my own design as a prototype for possible sales, what steps would I need to take to get an airworthiness certificate from the FAA? If it's truly a certified aircraft and not a homebuilt?
You can't legally fly any aircraft heavier than an ultralight unless it is certified. Your prototype will be certified as Experimental Category in one of these classes. The certification is awarded based on inspection during construction, on completion, and after a flight test period. The design is not subject to FAA approval.
If you want to manufacture aircraft for sale, you need approval of the design. This is called a Type Certificate. For smaller general aviation aircraft the appropriate regulation is Part 23 which states the requirements. There are also Advisory Circulars which provide clarification on approved means for satisfying the design requirements.
To avoid the expense of inspecting and flight testing every aircraft as is required for the experimental category, manufacturers instead obtain a production certificate. This reference is for larger part 21 aircraft. The production process is approved rather than inspecting each aircraft as it is produced. Each aircraft is still flight tested, but this may take an hour or less as compared to an Experimental flight test, which is 40 hours.
Reading these four references will give you some limited understanding of what you are asking. Here is an 2012 swag at certification costs. Part 23 was estimated at $$25m for design and testing, then another $25m for certification. This does not get you a production certificate.