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.
Many people are concerned about water damaging their basement and that fear keeps them from doing their basement project. While water can be a big problem, the cause of water is usually relatively simple to fix and most often not a reason to keep you from remodeling your basement.
Water usually leaks into your basement from one of these things:
Leaky Gutters. It's hard to believe how often gutters are left to hang off the side of a house, leaving a gap for water to flow directly into the house foundation and then into the basement. Always keep your gutters cleaned and attached firmly to your house, and if you have some water coming into your basement, the first place you should look is the gutter outside.
Gutter Drainage. If water is running properly down gutters, there will be significant amounts to deal with. Make sure the water is being diverted far away and downhill from your house. There's little point to gutters if all the water is channeled right to the foundation of our house and into your basement.
Neighbors Gutters/Roof. In some cases water is running from a neighbor's house straight into another foundation. If your gutters are good, check your neighbor's.
Sloping Lot. Houses on slopes cause the biggest basement water problems. Water runs downhill and if your house is on that hill, water will want to run into your foundation. This is usually when people have french drains installed, which is basically a channel of gravel along your foundation that moves water away and past your house. This gets a bit more expensive, but usually not enough so to deter people from making a safe investment in their basement remodel.
And always remember, if your basement has water problems, they always need to fixed from the outside. Even if you do your project and later have water, the majority of the work will come on the outside of the house.