If you are using extract, especially if this is your first time doing root beer, just follow the directions on the instruction sheet that comes with it. Mix your sugar and extract together along with your yeast. The directions call for ordinary bread yeast which works fine since it is only for carbonation. Make sure your bottles are sanitized. Fill them and let them sit at room temperature for about a week. From that point on keep them refrigerated, otherwise you will have bottle bombs.
The best way to tell when they are fully carbonated is to fill one plastic soft drink bottle with the root beer. Every couple days give it a squeeze. Once it is hard, it's time to refrigerate the batch.
Wayne