When you first start using Cocktail Party, you'll notice that the ingredients in each recipe have a line through them:

The line means that Cocktail Party thinks you don't have that ingredient in your library, and consequently, that you can't make this drink.

If you do have any (or all) of those ingredients, tap the square checkbox to the left of the ingredient to tell Cocktail Party that you own it:

Cocktail Party will update your library, and once you've added enough ingredients, Cocktail Party will show you the drinks you can make with the ingredients you have.