Don't try to look smarter than you actually are. A smart girl is often very attentive and will see through any charades. Act normally and keep the conversation flowing. Share knowledge that adds to the conversation; don't make up anything or pretend to know things that you don't.
Avoid excessive fawning. An intelligent, young woman isn't looking for a guy to smother her with compliments, especially about her intelligence. Constantly telling her how smart she is may sound condescending, pretentious or make you look like you aren't used to being around smart people.
Be open-minded and curious. If there's something you don't know about, ask. This doesn't mean to inquire about every point, but appear brain hungry. Show that you're interested in the knowledge she possesses.
Bring up topics in which you are well versed. For example, if you're an adept carpenter or a computer virtuoso, tell her about a recent project while avoiding the nitty gritty details. Present enough information to be interesting, without going into such detail as to completely lose her.
Spend a lot of time at a library or bookstore. These are ideal locations to meet smart girls, and by simply being there, you might gain some bonus points. When it comes time to plan a first date, try choosing a similarly intellectual setting, such as a cafe that hosts poetry readings.