This is one method of preparing absinthe: pour it over a sugar cube (or sugar) which you then light on fire to caramelize it. Then, mix with water. A sugar cube would work better than the loose sugar that I used, since it will burn longer (and caramelize more thoroughly.)
The more traditional method is simply to run a slow stream of water over ice, called "louching" which creates the same beautiful clouding of the Absinthe liquor. Here's a Youtube video
showing that method.