This is a Jean-Georges Vongerichten recipe. Essentially you are making the syrup (somewhat concentrated) and then adding it to soda water (club soda).
1lb fresh Ginger- unpeeled, cubed
2 stalks lemongrass- trimmed, chopped
2 small chilis- stems removed
1 1/2 cups sugar
1 Quart Water
Take the ginger, lemongrass, and chilis and process down until minced. Put them in a pot along with the quart of water and all of the sugar. Bring to a boil, then lower the heat to a simmer. Let simmer for about 15 minutes. At that point, remove from heat and then strain out the liquid. This is then placed in the refrigerator until chilled. You then take a glass of ice, pour in 1/4 cup of the syrup and then fill the rest with club soda. Lime slices are optional.
For my mixture, I cut down to 1 pepper, still had a nice spice to it. Also tastes very good with little bit of rum added (I used a single barrel non-spiced rum).