Weed and feed by scotts will take care of that. But you'll have a ton of empty dirt you will need to enrich/ reseed/resod.

If I water and fertilize the grass will it eventually crowd out the weeds? I realize this would take a very long time, but is that a viable option if I don't mind waiting?

Most here don't like weed n feed products. Best to use something like weed b gone and then follow up with a feed 5(?) days later.

St Augustine needs a very specific herbicide so you don't kill the St Aug. I'm not familiar with Scott's products for southern lawns, but, as neilaz said, use a fertilizer to fertilize and a liquid herbicide to spot spray weeds. But contrary to what neilaz said, Weed B Gone is not the product. It will kill St Aug. Weed B Gone is great for any other grass; just not St Aug.

No, St Aug will not crowd out broadleaf weeds. It will do a pretty good job with bermuda but some other grassy weeds give it trouble. You are in luck, though, there is a very effective herbicide. This one

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DANG. I didn't realize that picture was that huge!!
If you use it right (shake first and then spray as a mist) it works very well. If you use too much the St Aug will yellow for a week or so before coming back. But the weeds will not come back.

When the weeds die out, you can buy a few flats of St Aug and scatter them around in the bare spots. Keep them watered well for the first 3 weeks until the roots knit in with the underlying soil. Then start to back off. Use organic fertilizer like alfalfa pellets (rabbit chow) heavily and the St Aug will spread about 5 feet in all directions. Then in the fall after the hot weather is over, it will spread another 5 feet in all directions. You should have pretty good coverage, if not density, by November. Then next year the density will catch up due to the spreading in among itself. Key is to never let it dry out. St Aug does not go dormant like some other grasses. When it dries out it goes straight to dead.

Water it deeply and infrequently. Deeply means a full inch all at one time. Infrequently means monthly in the winter transitioning to weekly in the hottest heat of summer. If you have particularly dry and windy days that evaporate the water more quickly, you might have to go to a 5-day schedule. Once the grass is established, there is never a case where you should water daily for a few minutes at a time.

I use an oscillator type sprinkler - the new turbine drives, not the old mechanical linkage. These things are great. They provide a very slow application. Mine takes 8 full hours to get an inch of water. Your timing will vary depending on humidity, wind, soil type, grass height, shade, clouds, and temperature. Oh and raise your mower all the way to the highest setting for St Augustine. It looks much more plush and needs much less water.

I have a St Aug experiment going on. It has not been mowed since October of 2011. In some places the grass height is 30 inches. And in those places it has not been watered since Oct 2011. Here is a pic of that.

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Yes I know...pretty funny to see St Augustine that tall. It's an experiment, not neglect. Notice there are no weeds either. My yard is surrounded by weeds, so that is one of the results of the tall grass experiment.

dchall, thanks for the info...I will try this. One more question. I had some sod put down in one area last July - not a good time but a lawn company installed a drain and had to put something down. I watered it a half hour every day for a month and some of it lived and some of it died. You can see in the photo the live grass surrounded by dead grass, all installed at the same time and all got the same treatment. I was hoping the grass that died would come back, but sounds like from what you said it won't come back. Is there nothing I can do to bring it back?

I'm guessing the sod that went down was dead when it hit the ground. Or you might have flooded it and it died from a disease. 1/2 hour per day is too long if you have a 'normal' sprinkler system. 5-10 minutes per application, 3x per day, is more normal for new sod. Then back waaaay off on the frequency and water longer. It should spread 5 feet in the spring and 5 in the fall.

Water deeply and infrequently.

Mulch mow at the mower's highest setting.

Fertilize with alfalfa pellets once a month (or so) at 20 pounds per 1,000 square feet. Do this until the summer heat hits and start again on Labor Day. This is more often than you'll need it but in the case of organic ferts, more is better.