Start by reading this topic:
http://www.dirtdoctor.com/forum/viewtopic.php?t=382
The St. Augustine will take over most of the weeds as you improve your soil. Probably one of the best things to do now is to lay down a thin layer of screened compost over your yard. Some molasses (liquid or dry) will also help to jump start things. In the fall apply Corn Gluten Meal (CGM) for fertilizer and Spring weed control. In early Spring apply more CGM for the summer weeds and to give your lawn a good start. I water at the most once a week, very deeply. I usually water after I mow, and pull weeds the following day. There is much more information in the Lawn Care Forum that would be helpful to you.
I hope this helps