I am making myself a DIY 3D printer on a budget. And I don't know how to prototype it or design it. Like, I have already planned the parts. But, I don't yet have planned the structure or how parts should go together. I tried using a CAD software, but learning one to reach a skill that is needed will take a long time. I want to know how others design their printers and learn from that.
There are lots of ways from mere specifications to designs. Most follow several of the principles below, but designing a printer is not a light undertaking. it's HUGE.
Copy and adapt
The most easy way is to take a known design, for example from the RepRap wiki, and copy it verbatim. But it can easily undergo some adaptions, like different hotends or bed sizes.
Paper sketch & notes
Writing down the specs of some parts is very important to make sure these stay consistent. Paper is also the tool of choice for initial sketches or even finished designs to guide building the actual parts.
CAD is an almost indispensable tool to map out the placement of parts and combine them. Or later design parts to print. A CAD design doesn't need to be detailed, it can use stand in rough outlines. Only where parts need to be custom-made, details are essential.
All projects go through prototyping when groups of parts are built and tested on their own and combined piece by piece. Also, this step is where you finalize the firmware.