This traditional method of ingesting absinthe dates back to at least the 19th century, if not earlier. Other Drip recipes will tell you to caramelize the sugar with flame. Ignore them. The flaming technique is a relatively recent aberration and may have come about as a way to mask the repellent taste of inferior absinthe or its substitutes.
1 oz absinthe
2 - 3 oz ice water
1 sugar cube
Pour the absinthe into an absinthe or cocktail glass. Set an absinthe spoon across the top of the glass and place the sugar cube on it. SLOWLY drip the ice water onto the sugar cube until it completely dissolves into the glass.
The cold water will create a reaction in the absinthe called "louching," by which the absinthe turns milky and opaque. This is desirable. In fact, it's thought by many that the more dramatic the louche effect, the better quality the absinthe. The louche also serves to release delightful herbal aromas.