Hmmmm, sounds like somebody should read both Speak and The Lovely Bones. Those two books will answer your question. Both written in "teen-speak" and spoken by intelligent, teenage-girl narrators, ... there could be no better answer than for you to read those two novels.
Both characters are incredibly introspective, ... of course the subject matter is quite different. Ironically, neither deal with the subject that you so sarcastically suggested: love. Speak deals with the reasoning behind why the narrator decided to stop using words to communicate. The Lovely Bones covers the death and afterlife of a teen girl who was raped and murdered.
Of course, I am talking to you about characters from our general time period. It's possible (considering the context of your question) that you could be referring to a different time period entirely. For example, I wouldn't expect the narrator from a modern novel to speak, let's say, in Shakespearean English or Old English. However, if we were speaking about the character Juliet, ... I would certainly expect her to speak that way! I would also not expect a modern teenage girl to use words that an educational elite would use (i.e. not a whole lot of words like "plethora" and "rudimentary" and "derelict" and "befuddled" and "stymied." Similarly, I wouldn't expect her to use the simplified language of a five-year-old, either. Her speech would have to fit her age and ability level, ... possibly someone who would be found in your advanced literature class. I would also not expect, considering your question was written in English, that this girl would speak in French, Italian, or Swahili.
In short, read the two novels I mentioned above; however, if you don't have the time for that, just look beside you in Honors English and listen to the girl sitting next to you. Ponder how she speaks. That is what your narrator should sound like.
From a narrator of this nature I would expect a lot of introspective narrative in the form of a stream of consciousness. I would expect analytical terminology that reflects a high ability for comparison and contrast, and imagery that is both complex and thorough. It is certainly clear that a young, gifted individual is different from others in their ability to create constructs of thought and in their ease for verbal and analytical expression. They effortlessly can view and interpret things from different perspectives and are comfortable with the use of a complex and varied vocabulary.
Depending on the context of the teenager, in terms of geographical location and social class, both of which are incredibly important elements, you would expect such a girl to speak using educated langauge that is not too erudite or sophisticated. She would definitely not use slang or crude phrases or terms. Her language would of course reflect her outlook on the world and her personal identity.
I think by language you are referring to the way the narrator usese words. An intelligent teenager uses words like an adult, but still has some of the feelings and sensitivities of a child. As a teenager, she is still experiencing a great deal of angst. However since she is intelligent she has the words to describe it.
I don't know if you are referring to a specific character in a novel or if you are asking about that kind of character in general, so I will give you a few ideas that might be applicable to that kind of stereotypical girl. Your teacher is asking you to think about "language" so you should be thinking about vocabulary (word choices) and syntax (sentence structure; sentence types). If the young lady is intelligent, then she is likely to have a large and varied vocabulary. She would use precise word choices to describe the people and things she observes in her world. An author who is creating this character is likely to use more difficult vocabulary -- less "ordinary." For example, the character may observe that someone is loquacious -- a fancy word for talkative. The character might say that the person is garrulous. Again, it means talkative, but it suggests someone who talks excessively about trivial matters. An intelligent character would use the best word with the best connotation.
In regards to syntax, the character would likely speak in longer sentences and with varied sentence patterns. There would be an interesting mix of the sentences with dependent and independent clauses and various types of phrases used in different patterns. Thoughts would be well-developed and made clear to the reader.
Because the character is also sensitive, the character is likely to reveal her understanding of her own emotional response to events and people, as well as intuit the feelings of others in a situation. She will pay attention to detail and draw logical conclusions about the various events going on around her. Sensitive doesn't necessarily mean weak, but it could be that she is more fragile than others.
Hope this gives you a place to start your evaulation of a character!
shes anlways gonna talk about love