People are often intimidated by the city and their processes for ADUs. In general, cities are usually fairly helpful with homeowners interested in undertaking an ADU project, and ADU basements are the usually the easiest kind.
The first thing to do is visit the web site of your city's building and planning department and download any materials you can find regarding ADU rules. Read all of it. Twice. Without much context not everything will sink in and much of it won't apply to you. But the things you do remember and those that might apply to you will help you ask better questions.
Now that you have a good list of starting questions, it's a good idea to sketch out your basement on paper. It doesn't have to be too fancy, just showing the dimensions, ceiling height, and locations for windows, doors, furnace, water heater, electrical panel, etc.
With these two steps completed, head down to your local office and show them what you have. You'll also probably have a list of questions like "will I have to move my electrical panel" or "does the stairway down to the basement have enough headroom?" Keep in mind, they will generally only answer questions and not volunteer much, so the more you ask, the better.
If you want to get the permits on your own, you'll probably make at least 2-3 trips to the city, each time improving what you present to them and each time armed with better questions. At the end of this process, you should have a drawing that is stamped for approval like the one above, which was the plan for my personal basement ADU.