The trick is that soda is not fermented dry like beer is. There is generally more fermentable sugar than you need for carbonation, so it will keep fermenting and raising the pressure until you stop it. If you don't stop it soon enough, it over-carbonates and you get bottle bombs. You generally stop (or at least drastically slow down) the fermentation by putting the bottles in the fridge when they feel pressurized enough. You are using plastic bottles, right? They should end up feeling about as hard as a plastic bottle of commercial soda, at which point you chill them and keep them cold. This is usually a matter of days, not weeks.
I make my sodas in one-gallon batches. The recipe basically goes like this:
2 cups brown sugar
3 Tbsp malto dextrine (for mouthfeel, not really a necessity)
4 tsp or so root beer extract from the grocery store
1/2 tsp vanilla extract
1/2 tsp anise extract
1/4 tsp champagne yeast
And the rest is water.
Mix the sugar, malto dextrine, extracts, and most of the water until everything is dissolved. You may want to heat the water to get the malto dextrine to dissolve. Rehydrate the yeast in some warm water. When everything is at a good temperature, add the yeast-water and aerate the mixture. Transfer to plastic bottles, cap them, and let them sit somewhere to ferment. Check them once a day, and when they are hard like normal soda bottles, stick them in the fridge. If you forget about them while they are fermenting, they will explode.