When the invitation says cocktail attire, a teenage girl should opt for a dress that is appropriate but still stylish. A knee-length dress, such as a sheath or shift dress, is a suitable option. For a more formal look, try an elegant lace or velvet dress. A tailored blazer or wrap dress can also work as cocktail attire. Accessorize with statement jewelry and a pair of pointed-toe heels to complete the outfit.