Many men get very intimidated when trying to talk to an attractive woman, and this nervousness can interfere with making a good first impression. If the first discussion does not go well, it is much less likely the girl will be interested in going on a date or otherwise pursuing social interaction. Talking to a pretty girl is really no different from talking to someone you're not as attracted to, but you need to control your nerves and approach the situation with confidence to increase your chances of getting a date and impressing her.
Smile as you approach her. If you look nervous or distressed, you're already sending out the wrong signal to her. You need to address her as an equal. A warm smile is one of the first things she'll notice and can open the door to a conversation. She's also more likely to smile back in response, which can put her more at ease.
Make eye contact with her. This displays both confidence and respect. If your eyes wander, you could appear disinterested or nervous, and she might construe that as apathy. Pretty girls are often used to men acting anxiously around them, so meeting her gaze and holding it can set you apart from others that she's talked to in the past.
Compliment a specific feature about her, such as her eyes, her smile or a specific piece of jewelry that she has on. She'll ideally be flattered, and this opens up the potential for further conversation. Avoid complimenting her body, because that could come off as weird or sleazy if she doesn't know you.
Tell her a joke to demonstrate your sense of humor. If she is very attractive, she likely has her pick of many available men, but a sense of humor is what often sets a man apart and makes him more appealing. Avoid turning the conversation into a standup comedy session, but joking around is important early on.
Ask her questions about herself. She's probably used to others who focus only on her looks, so she will likely be impressed that you are taking a deeper interest. Learning more about her background, education and other attributes can lead to a date or further interaction down the road as you both figure out if you have a genuine connection.
Listen to her. By paying attention to what she tells you, you can remember details about her life and follow up on them as the conversation continues.