The paperwork to start a business is daunting and only a lawyer can provide you with sound advice for ensuring you have your ducks in a row. This page, you'll note, doesn't have a law degree and thus you shouldn't rely on it for legal advice. That being said, it may be a useful place to start collecting at least some of the required resources for.
To be clear: California is often considered the most difficult state in the United States to start and maintain a business in terms of paperwork and requirements (the territories are even worse, but that's small comfort if you want to sell your grandmother's famous pastries at the Farmers Market). For the gritty details, you really need to do some serious reading and consult experts.
A Business License from the city finance department is needed by most commercial enterprises in town, in part to track taxes on commercial transactions and services. Some also need a Fictitious Business Name registered with the county or a bond to insure their work.
You can use the Business Directory to look up existing businesses in Davis, but it is not always up to date.
If you're going into business, get informed: look over Chapter 19 of the city code and know your rights and responsibilities.
If you're registered with the city, then you probably don't need a Yolo County specific license.
However, regardless of whether or not you need a license you will likely need to file a Fictitious Business Name with the county if you're not using only your real name to do business by.
And then, if you're selling stuff (including services) you likely need to file with the state of California's Board of Equalization for a sellers permit.
And if that wasn't enough, some businesses need state licenses for doing certain types of jobs.
And, of course, there are state income taxes to worry about.
The federal government likes to collect income taxes from businesses too.
There are also many many other things like ADA compliance, posted notice requirements, field specific licences like contractors or the BEAR license and more. You might have to sacrifice some blood red flowers and berries to Sredni Vashtar. But when all is said and done, it can be an enormously satisfying feeling to run your own business.