Preparation

While the most popular way to enjoy absinthe is an Absinthe Drip created by adding 1:3 or 1:5 parts absinthe to ice water (with or without sugar). Absinthe has long been known as a required ingredient in many classic cocktails and enjoyed in a wide variety of ways. Here are few examples of how absinthe was enjoyed in the USA before, during and after prohibition:

Butterfly Absinthe Louche

 

The Cocktail Book: A Sideboard Manual For Gentlemen
1926

Absinthe Cocktail (Use mixing glass)
Two dashes Angostura bitters; two dashes gum syrup; one pony absinthe.
Fill with ice, mix well, and strain into a cocktail glass.

Absinthe Frappe (Use mixing glass)
One pony absinthe. Fill glass with fine ice, shake well, and strain into a cocktail glass.

California Absinthe (Use mixing glass)
One pony absinthe. Fill glass with fine ice. Shake well, strain into star champagne glass, and fill with siphon.

The Mixicologist
1895

Absinthe Cocktail (Use medium-sized glass)
Fill glass nearly full fine ice; cool off claret-glass while preparing. Take 2 dashes Angostura bitters, 2 dashes anisette, 2/3 jigger absinthe. Add a little water; stir well, and strain into claret-glass.

Absinthe Frappe
Fill mixing-glass with fine ice, one jigger absinthe, a few drips of anisette; shake well, strain in claret-glass and fill with Seltzer.

Dripped Absinthe
Put pony-glass in mixing-glass, fill around with fine ice, fill pony with absinthe drip about two jiggers water through drip in absinthe, running over the sides of the pony; then take out pony and stir; strain in port-wine glass.

The New and Improved Illustrated Bartenders Manual; Or: How to Mix Drinks of the Present Style
1888

Absinthe Cocktail (Use a large bar glass.)
Fill up with ice;
3 or 4 dashes of gum syrup;
1 dash of bitters(Bolter’s genuine only);
1 dash of anisette;
¼ wine glass of water;
¾ wine glass of Absinthe; shake well until almost frozen, strain it into a fancy cocktail glass j squeeze a lemon peel on top, and serve. This drink is liked by the French and Americans, it is an elegant beverage and a splendid appetizer, but see that you always have only the genuine Absinthe for mixing this drink.

How to Mix Absinthe (Use an Absinthe glass.)
Mix as follows in a large bar or Absinthe glass: 1 pony glass of Absinthe, place this into the large glass, take the top part of the Absinthe glass, which has the shape of a bowl, with a small round hole in the bottom, fill this with fine shaved ice, and water; then raise the bowl up high, and let the water run or drip into the glass containing the Absinthe; the color of the Absinthe will show when to stop; then pour into the large glass and serve. None but genuine Absinthe should be used, which you can easily tell by the color in mixing, as it will turn to a milk color and look cloudy, which the domestic article does not.* This is what they call an old style French Absinthe.

*Butterfly does.  This report shows that some of the other pre-ban American absinthes had trouble louching. This is not the case with Butterfly Absinthe.

American Style of Mixing Absinthe (Use a large bar glass.)
¾ glassful of fine ice;
6 or 7 dashes of gum syrup;
1 pony glass of Absinthe;
2 wine glasses water;
Then shake the ingredients, until the outside of the shaker is covered with ice; then strain it into a large bar glass and serve. As this is mixed it is more pleasant to drink than the French style. The Americans are not in the habit of drinking Absinthe like the French, but a drink of it occasionally will hurt nobody.

Italian Style of Mixing Absinthe (Use a large bar glass.)
1 pony glass of Absinthe;
2 or 3 lumps of broken ice;
2 or 3 dashes of Maraschino;
½ pony glass of Anisette;
Take a small pitcher of ice water, and pour the water slowly into a large bar glass containing the mixture, stir with a spoon and serve. This is a very pleasant way of drinking Absinthe. As it promotes appetite, it is especially recommended before meals.

German or Swiss Style of Mixing Absinthe (Use a large bar glass.)
The Germans and Swiss have the simplest way of drinking Absinthe that I met with in my travels through Europe. If a person goes to a cafe or barroom as we call it, and asks for Absinthe, the bartender or waiter puts a pony glass of Absinthe into a large tumbler and sends this and a pitcher of water to the customer, who helps himself to as much water as he desires, and there is no mixing or fixing up about it. I consider this a very simple style of drinking Absinthe, but it tastes good to them and answers the purpose.