St Augustine is different from other grasses when it comes to herbicide. On one hand it can handle lots of salt but it cannot handle the normal broadleaf herbicides tolerated by every other grass. So you cannot use normal Weed-B-Gone with it. The weed killer you need has atrazine in it. You can only use atrazine products one time per year, so be sure you're doing it right.

Spectracide's weed product for St Aug looks like this...

{{gwi:86656}}

This particular bottle is easy to use. All you do is connect the hose and go. About a week before you spray, water the lawn heavily. Apply about an inch of water on Saturday and spray the herbicide on the next Saturday. Weeds dies best when they are fairly healthy. When you spray, stretch the hose all the way out to the farthest reach you want to spray and work your way, backwards, away from where you've sprayed. DO NOT walk through this stuff or let the pets on it. Atrazine is nasty stuff. All you have to do is mist the leaves, not drench the soil. And you might not see results immediately...or even in a week, but in 3 weeks, all of a sudden, you'll notice no more weeds.

Now that I think about it, I would leave your current weeds the way they are and wait until spring to spray this stuff. Since it says to only spray once a year, why not spray to kill out all the summer weeds? I'm thinking late April would be good in most of LA. That will give the St Aug the rest of spring to refill where the weeds were and all summer to enjoy.

As for fertilizer, I'm an organic guy. I haven't used a chemical fertilizer in 11 years. If you want a recommendation about organics, then apply alfalfa pellets (rabbit chow) at a rate of 10 pounds per 1,000 square feet now. In 3 weeks, apply again at 20 pounds per 1,000 square feet. That will take care of your fertilizer for the winter.

If you are not mowing at your mower's highest setting, start that now. St Aug will always be weedy when mowed too low.

And if you are watering more frequently than once per month this time of year, you should wean your grass from the frequent watering to watering much less often. When you do water, apply 1 inch as measured by tuna or cat food cans.