Here is the recipe I use from my Amish neighbor, Tana! :]
Old Fashioned Amish Rootbeer:
1 tsp dry yeast
1/2c warm water
2c granulated (white) sugar
1qt hot water
4tsp rootbeer extract*
Dissolve the yeast in the 1/2c warm water for 5 minutes. Dissolve the sugar in the quart of hot water while yeast dissolves. Mix together the dissolved yeast, sugar and rootbeer extract in a gallon jar. Fill the jar with warm water and stir until all ingredients are mixed. Cover jar and set in the sun for at least 4 hours. Let sit inside overnight then chill before serving.
I only set mine out during the summer, the rest of the year it sits on my kitchen counter overnight and it turns out exactly the same. This is NOT sugary sweet like the soda they sell in bottles! Also you can buy a rootbeer extract at most grocery stores, but I go one step further and make my own. I got the recipe off this website.
*Rootbeer Extract (from Foodie with Family Blog):
3oz dried sassafras root
1/2oz dried burdock root
1tsp dried whole coriander seeds
1 whole star anise
1 whole clove
1/4 cup dark molasses (not blackstrap)
3-4 wintergreen leaves or 2 drops (or 1/8 of a teaspoon) wintergreen flavouring or extract
up to 6 cups of sugar (preferably raw, but granulated white sugar can be used.)
Put the sassafras and burdock roots, coriander seeds, star anise and clove in a heavy-bottomed 2 quart saucepan that has a tight fitting lid. Pour the water over the top of the roots and spices and bring to a boil over high heat. Drop the heat to low and simmer for 15 minutes. If it keeps bubbling up and out, vent the lid just a bit.
Add the molasses, stir, replace the lid, and return to a simmer for 5 minutes. Remove the pan from the heat, add the wintergreen flavouring or extract, replace the lid and let the mixture cool to room temperature. (I let mine cool on a cold burner on the stove overnight because I prepared my sassafras infusion late at night.)
Line a fine mesh strainer with cheesecloth, place over a large measuring cup with a pouring spout or a pitcher, and pour the cooled infusion into it to strain. Do not press on the contents, but let the roots rest in the strainer for about 30 minutes before proceeding. While that strains, rinse the pot in which you infused it to get any lingering bits of root or spice out of it.
Measure your sassafras infusion, return it to the rinsed pot and add an equal amount of sugar -by volume- to the pot. For instance, if you have 4 1/2 cups of infusion, add 4 1/2 cups of sugar. Bring the mixture to a boil, drop the heat to low and let simmer for 5 minutes. Pour the syrup into canning jars, fix clean, new, two-piece lids on top and store in the refrigerator up to a year.
I prefer my rootbeer with the homemade extract, but my father makes his with McCormick rootbeer extract and it tastes just as good.