The act itself of design is one of problem solving, and so unfortunately there's no formulaic, consistent set of steps. With every new problem, a new solution is required, and each solution is some combination of the tools you have at your disposal. That said, there are strategies that can help you think about the problem, to explore it and break it down into smaller problems. Design problems are most challenging when they're big and impenetrable - and so, strategies for getting in there and getting your brain working through it can be quite valuable.

One I use very frequently is asking myself questions about the problem, or about the context in which the problem is meant to be solved. Our designs don't exist in a vacuum - they are implemented by characters, in a world, and those characters have access to certain technologies, or have certain cultural drivers, and the world - the physical location, the time period, etc. impact all of these things. Asking yourself questions is a good way to crack open a problem and flesh it out, and every answer leads either to new problems, or gives you something to include in your design.

Something as simple as a question of "hey do these people have access to glue" can lead to a ton of simple details, like rivets, nails, brackets, belts, etc. that you may never have considered.

This is a video I made for Proko's Channel a few years back - it's pretty short, but it goes into this in more detail.