California Clay?
Answers:
I've been gardening in California for years and have encountered all sorts of soil types, including the "lovely" clay of sonoma county. You can not dig it when it is too wet, or the stuff turns into big lumps. You must wait for it to dry out just enough so you turn it and incorporate all sorts of organic matter. Leaves, manures, compost, as much as you can get. Like a 6 inch thick layer, then dig it in.
Currently, I live in the hills where decomposing granite is the "soil" and this stuff is like cement when it is dry. Undiggable.A shovel doesn't even go in one inch. One must dig only when it is wet, and drip lines are the key. Again, incorporating as much organic material is crucial: manures, leaves, compost. This soil also benefits from soil sulphur. In desert cement, adding lots of fertilizer is crucial to a successful garden, as desert soils are lacking in just about everything a garden plant needs.
This fall, go through your town and pick up as many bags of leaves that people set out for trash collection as you can. That's how I got most of my free material to improve my soil. Hundreds of bags of leaves every fall for 3 winters did wonders to my soil. I can now dig (certain areas) and grow vegetables that survive.
Another thing that will improve your soil dramatically, is to take all you kitchen vegetable waste and bury it in the garden. This is sheet composting, and where you want a garden to be you dig a trench (3 feet long, a shovel deep and wide) and each day you toss in the kitchen scraps, then cover that part of the trench with a little soil. You can add grass clippings and leaves if you have them, too. Just bury the stuff, mound it in one place then put dirt on top. In a number of months you will have an instant raised bed and can plant directly in it about 2 months after the scraps were added. The areas of my garden where I have buried kitchen scraps grow the best vegetables, and now is diggable soil.
It takes time and effort, but you can have a good garden in bad soil.
Other answers:
A lot of organic matter such as compost will go a long way. If you're in Southern California, then peat moss will be good, as it also helps to acidify the otherwise alkaline soil. Also, Gypsum will help shorter term to help drainage, but it doesn't really help with the soil long term. So, a combination of compost, peat moss, and a little gypsum. Work a 3-4" layer of compost in 8-12".
A lot of organic matter such as compost will go a long way. If you're in Southern California, then peat moss will be good, as it also helps to acidify the otherwise alkaline soil. Also, Gypsum will help shorter term to help drainage, but it doesn't really help with the soil long term. So, a combination of compost, peat moss, and a little gypsum. Work a 3-4" layer of compost in 8-12".