Eggs are used in many liqueurs, but also in some drinks and punches. When a recipe call for eggs, large (grade AA) chicken eggs should be used.
It is generally a good idea to break the egg into a small bowl or cup before using it. That way it is easier to remove pieces of shell that break off, and a egg that has gone bad won't spoil the drink.
Warning: In many countries eggs contain salmonella. This bacteria can result in food-poisoning, and could be lethal to persons with a compromised immune system. Use replacements such as egg powder or pasteurized eggs if this is a problem where you live.
Separating eggs (separating the yolk from the white) is easier if the egg is cold. This can be done by using an egg separator, or by cracking the egg into a funnel over a bowl (the white will fall through, but the yolk won't). It is also possible to separate eggs by passing the yolk back and forth from one half of the shell to the other, while letting the white slip into a bowl. However, with this method there is a greater risk that bacteria can transfer from the shell's surface to the raw egg.
Egg whites are usually added to a drink to make it frothy when shaken or blended. There are several substitutes available, such as Frothee, if you do not wish to use raw egg whites.
To be able to divide an egg white (i.e. when a recipe call for one tablespoon) you can beat the egg white slightly with a fork first. That will make the white more liquid and easier to handle.