I would suggest the first thing is just to spend time reading about it as an interested layperson. Histories of rocketry, Hayne's manuals, payload user's guides and Wikipedia articles about specific rockets and systems, go to YouTube and find Scott Manley, Everyday Astronaut, and Curious Droid. How do the engines actually work, what kinds of fuels are used, how do they steer, and so on. Be able to talk about rockets in general. That will take time, of course.
In the real world the next step is to identify the mission and explain why an existing launcher is not suitable, or what market niche your startup will occupy so that it can operate profitably. You'll have different requirements for sending a rover to Mars versus a small payload to low earth orbit, or, perhaps, five small payloads to distinct orbits.
Uhoh has a nice list. But if I were an engineering student going through a design process I'd begin with how much mass must be lifted into which orbit and estimate fuel requirements and size from that. You'll have to start making some decisions, like a first stage fueled by RP-1 and LOX using a gas generator cycle? (Look up the specs for SpaceX's Falcon 9 and Merlin engine.) Same for the upper stage? (Look up Falcon 9 upper stage.) A liquid hydrogen and LOX upper stage? (Look up the Centaur.) You won't go far wrong if you base your numbers on existing, successful technologies.
With that as a rough guide, go through Uhoh's list. Nobody can really design it all. Different people will be working on engines, guidance, and so on. But you can at least identify the parts and make some reasonable selections.