Attractive women are approached in one way or another all day long, and you can almost guarantee that even a moderately attractive woman has heard plenty of lines from different men. While some guys just don't have the confidence to approach attractive women, others are just intimidated by their beauty and literally become immobilized when they see one they'd like to meet.
Most of the anxiety involved in approaching attractive women comes from the fear of the unknown and the fear of embarrassment or rejection. In order to approach and be successful with attractive women, you need to have total confidence in yourself and teach your mind and body not to be afraid of them. By acting as if you have no confidence in yourself, you eliminate yourself from a woman's list of potential dates.
Make it a point to approach an attractive woman as if you didn't go out of your way--because if it looks like you made an effort to speak to her, you'll seem desperate and turn her off before you even get started talking.
Relax, introduce yourself, ask her name and try to give the impression that you are interested in her and could see the two of you hitting it off, while keeping in mind not to treat her as if she's some queen that you should praise and lower yourself to. Always speak intelligently, be direct and show her that you're an honest guy that has the courage to come and talk to her without any desperate openers.
Engage in a conversation with her by talking to her as if she is an average woman. Don't introduce yourself by mentioning her looks or by eying her up and down. If she shows interest and talks to you, listen to her in order to determine if she is suited for you. Ask her questions about herself and listen to what she tells you and respond to her with further conversation based on the information she provided. Then you can lead the conversation to getting her number, etc.
If she says no or seems uninterested, do not pursue it any further. Walk away and don't take it personally. If she isn't interested and you're turned down, realize that it's a part of life and that not every kind of person mixes well together.
Overcoming rejection may be hard to do, but realize that you may have to go through a lot to find a good woman who is accepting of you. Who knows--the next attractive woman that you see may actually want to get to know you and could be waiting on you to approach her, but you will never know if you don't overcome your fear and make the first move.