First a word of caution this recipe uses sugar and yeast and if you don't watch out you will make alcohol. The longer you let it get away from you the more alcohol that will be made.
While bringing the gallon of water to boil make Lemon Zest from the two lemons and add it to the water. Lemon zest is made by grating the yellow part of the rind of the lemon with a fine grater, leave the white part of the rind. Grate the ginger and add it to the water. Squeeze the lemons and add to the water, about 1/2 cup of juice. Add the cinnamon stick or a few cloves to the water. When the water boils add 2 cups of sugar. Make sure the sugar dissolves and remove the cooking pot from the heat. Options for you to try is to change the amounts of ginger, sugar, and lemon juice, adjust to your taste. Let the brew cool for about one hour. I took about 1/3 of a cup from the brew and made sure the liquid was only luke warm to my touch and add the yeast to this liquid. Let the yeast sit in this liquid for about an hour and then pour it into the main pot of brew. Cover the brew and let it sit 12 hour/ over night in a warm place . Strain the solids from the brew and put the liquid in plastic bottles. I like the plastic sport drink bottles with wide mouths. Leave them in a warm place until the bottle get rock hard from the pressure inside of them. My batch was done in 36 hours after inoculation with the yeast. The yeast now needs to be deactivated and the fastest way to do this is to chill them, put them into the fridge. Check the bottles after they have chilled down to see if they are still rock hard. You can take them out and warm them up if they are soft. The yeast will become active again if it warms up. Drink one if it is still rock hard. Enjoy your fine drink. The Ginger Beer will turn clear if you leave it in the fridge for a while with the sediment collecting on the bottom of the bottle. Important notes: Yeast and sugar will make alcohol if the yeast is left to ferment long enough. Yeast likes a warm environment but not a hot one try not to go over 95°F or you will start to kill the yeast off. Don't use glass bottles for your brew they can blow up. :( The plastic bottles will hold 60 to 80 PSI. Here is a link for you to read if you want to know more. http://www.leeners.com/rootbeer.html I don't agree with his comment about alcohol being made because yeast doesn't always make alcohol when there is sugar present. It takes the yeast a while to "Grow Up" before it will make alcohol. I'm going to take some of my Ginger Beer to work and test it for alcohol.