Really easy. Here's a recipe based on one from the Homemade Rootbeer (Stephen Cresswell) book, scaled down for 2 liters.
1.5 oz ginger
juice of 1/4 lemon
1/2 cup sugar
a pinch or more of cayenne pepper to taste (for the burn)
Grate the ginger into the brewpot, add the lemon juice, cayenne, and 1 liter/qt water and bring to a simmer. Add sugar, stir to dissolve, simmer 30 minutes, cover and cool 30 minutes.
Put 1 liter water in a 2-liter bottle, pour in the ginger mixture.
Top it up to where a normal soda bottle would be. Chill and force carbonate with a carb cap.
If you want to naturally carb and or like it sweeter you should use more sugar (3/4 to 1 cup total), I cut it back since I force carbonate mine and I like it less sweet.
Top off the jug, you want it to be lukewarm. Leave about 2 inches headspace. Cap and shake.
Rehydrate a pinch of ale (or baking) yeast in 1/4 cup lukewarm water, add to the jug, cap and shake again. Let it sit at room temp until it carbonates, chill when the bottle is firm, and consume quickly.