I am a cynic so I just wanted to put that disclaimer up front. I help run a large community garden in Sacramento, I run a small B&B, and am starting an urban farm on 1/2 acre as well. So I DO believe in this stuff but that said...
Notice the number of people mentioned who run non profits, develop "programs" and license people to teach them? THAT is the end that is an actual business. Farming is a great way to make a small fortune you just need to start with a larger one!
A few have mentioned Ron Finley's Urban Homestead, four people working solid hours making $20k? Even if you say the food they eat is double that, that is $10k a year per person. Its sad but working at McDonalds pays more!
Most of these farms are labors of love, meaning the owners and volunteers subsidize them with labor and love. They are not a sustainable business. Their quality of life can be high, the emotional rewards wonderful, and certainly far tastier and healthier food but the people buying the food? They work real jobs and make in Los Angeles probably close $100k a year to afford to buy CSA food.
I am NOT saying any of this to discourage you but you asked about BUSINESS, not how to enrich your soul or your soil...
The money (and its not much) in all of this is in teaching others to do what you want to do, getting grants to do what you want to do (thus all the non profits that pay salaries to their managers), and staffing the whole thing with volunteers. Growing and selling raw veggies is also the lowest rung of all this, there is very little value added. A local company here raised $100k on kickstarter to make organic bloody Mary mixes...value added!
Now I am NOT saying "money" is the goal but you do need it to buy water, seed, gas, and a roof over your head so it IS important, although all of us here have a different value on it than the rest of society.
MY plan, is to open a cafe downtown, grow the majority of the produce and some of the meat for it, teach classes on the "farm" and create our own sort of closed loop setup where each space makes the other "cooler" and we not only add value as things move up the chain but we keep it all in house. If it becomes a roaring success I won't have to have a full time job to support it, LOL!
So, my advice is to first decide how much you need to make to live, calculate how much you need to grow to achieve that, and then understand that water is only going to get more and more expensive in LA so you will need to invest in rainwater harvesting to offset that cost. Now THERE is something that could be interesting. Ask the neighbors if you can capture the runnoff from their houses as well. They don't use it and capturing it from three surrounding properties could produce a fair amount of water. Now its urban runnoff so you will need to divert a fair bit and let the remainder settle in tanks but that should only set you back $10k but that IS something crowdsourcing or grants could pay for.
Anyway, best of luck!