What are the steps for ADU

You need to have a design to submit in order to get the building permit. So you should do that first. Find an architect or a design/build firm with experience doing ADUs in Berkeley (so that they know the regs). They should be able to guide you through the permitting process. 

Yes, you need a permit no question (unless you are considering building illegally, which of course introduces problems you probably don’t want...) The permit process is a bit complicated; sometimes described as a nightmare actually. This has changed a bit since they are supposed to be encouraging ADU’s to be built. You can certainly file the permits yourself, but I think the norm is that the contractor will file them, and then of course the contractor deals with them on each step of the process where the permits are required (scheduling the inspections at the job site; corrections or changes after inspections, etc.). So the “guiding” is not really on you; it’s on the contractor, who knows it like the back of their hand. Try to hire an ADU builder who has experience building in the City of Berkeley. Two other unrelated suggestions - join BPOA, and familiarize yourself with the Rent Board. Your unit will be exempt due to the passage of Measure Q (or if you happen to be a Golden Duplex), but the Rent Board attempts to steadily erode this exempt status - good to pay attention to it. Good luck!

I went through the process about ten years ago, and built my accessory building. There were two stages then. Zoning stage followed by building permit stage. I managed the zoning stage by myself, but definitely needed architectural plans complete with engineering calculations, and lighting calculations to get approval for the building permit.  For the zoning permit I needed the footprint of the building, the height, lot coverage, etc. There have been many changes in ten years, however.