I'm a big fan of Sandor Katz who wrote Wild Fermentation, in fact his newest book the Art of Fermentation should be here this week.
I tried his recipe for Ginger Ale some time ago. It involves creating a "ginger bug" from ginger and sugar dependent on wild yeast from the environment. I ended up with a sticky mess after several days and lost interest.
We have been looking at making cheese and I discovered Fankhauser's Cheese Page. There are recipes there for both ginger ale and root beer. The recipe for ginger ale is nearly the same as the Wild Fermentation recipe except that instead of using wild yeast it uses cultured yeast.
I used a cup of sugar, a bit more than a tablespoon and a half of fresh grated ginger, the juice of one fresh squeezed lime and a quarter teaspoon of champagne yeast in two quarts of water. They use plastic two liter soda bottles. I used a half gallon glass growler bottle that I got from Tom, in fact I think I have three of those. I let it ferment under an air lock until the big bubbles stopped, three days I think. Then I strained and bottled it in two champagne bottles and a beer bottle. I left them at room temperature for two days. This morning I opened the little bottle. I should have chilled it first as I lost almost a quarter of it as it foamed out on the counter and the sink.
It is excellent and super simple. They say it is less than one percent alcohol. I need more champagne bottles as I will be making more of this. In the mean time I will make due with brown long neck beer bottles, also from Tom.
The recipe called for the juice of a lemon but I had a lime which resulted in a very refreshing taste. Next time I will try a lemon.
UPDATE 1/18 - The new book Art of Fermentation gives a possible cause for the failure to make a "ginger bug" from commercial ginger root. The book says that ginger root is irradiated to kill any bad bugs. Likely killing the multitudes of yeasty flora that would normally be present to create a proper "ginger bug". I have a new batch of ginger ale going using the same 1/4 tsp of champagne yeast. this time with a lemon. I think it will be great!