Here's a link to CA DMV to get you started:
CA DMV Vehicle Code Index. Scroll down to "IMPLEMENTS OF HUSBANDRY".
There's a small search field in the upper right-hand corner of all the DMV pages. You may want to use it after checking the index, because the index doesn't cover everything, for instance this one:
V C Section 24615 Slow Moving Vehicle Emblem.
Be prepared to feel frustration as you search and read. Search results seem rather erratic, ("tractor", "farm tractor", "implement of husbandry" will all get different results, none of them alone will get all the information you may want/need.) Documents are in legalize, as you might expect.
In brief, my understanding (and I am most definitely not a lawyer) is that you *do* need a Slow Moving Vehicle placard (if you're operating at less than 25 mph) at the rear of the vehicle or combination of vehicles (if you're towing a trailer the placard needs to be on the rear of the trailer), more than 3 feet above the ground, but no higher than 5 feet. You are *not* required to register or get a license plate (unless you have a really huge tractor, in which case you need a special permit, or maybe if you're operating faster than 25 mph), and you *may* (but are not required to) get an "Identification Plate" (I don't know what purpose this serves or why you would get one, but you can if you want.)
What I do: SMV placard placed permanently on the rear of the tractor, another that can be temporarily mounted on anything I might be towing. The only lights the tractor came with were headlights, so I use them and have some clamp-on flashing lights I mount on or near the placard or at the left rear. I don't know if they're legal or not, but I'd rather be seen than be legal. And I stick reflectors all over everything. I prefer not to be on the road after dusk, but sometimes things happen.
Hope this helps, and have fun reading that legal stuff. *Don't* take my word for it!