The first mistake you already made before you even started is that you believed that this person is out of your league. When you believe that, you will act according to this mindset. You must have confidence to let them know that you are as good as they are ... or even better. That's why step one is VERY IMPORTANT:
You must develop confidence. The first thing you need to do in order to attract someone out of your league is to believe that they are not out of your league at all. It is very important to know attraction can happen just about anywhere and with anyone. According to the psychology of attraction, people get attracted to those who have a higher total “score” than them or at least a similar one. So keep your eyes open to all possibilities.
Don’t worry about how much attention they get from the opposite sex. If you show interest that goes beyond the good looks and status, they will know recognize that. So, curb your outward signs of the fact you think they are drop dead gorgeous, and/or have status everyone wants. Smile, but don’t over-flirt. They already get plenty. And if you're faking it, they can spot that a mile away.
Know that you are dealing with a human being. This person has weaknesses, insecurities and fears that can be well-hidden behind their apparent resources and looks. If you are able to get to that level (without being obtrusive), there’s a really strong chance you have gone where only a few have gone before.
Status is perception dependent. You don't have to be extremely beautiful or extremely wealthy in order for people to think so; you just have to control people's perception. Be mysterious and only reveal little parts of the puzzle that would tempt the other person to build an imaginary perception of you. The human mind can't withstand curiosity, so let them be challenged to complete the puzzle by going after the missing info.
Use friends to alter perception. Surround yourself with friends who speak and act to build you up, NOT tear you down with the negative phrase, “they’re a little out of your league.” Positive energy will allow them to see you as a person of real value. In social settings with those supportive friends present, take advantage of any gatherings where everyone is clearly having fun.
Don't be a nice guy or girl, but don't challenge the person's ego too much either. There’s that confidence thing again. When you are talking with them, be comfortable in your own skin as you tell your story, allowing them to share theirs. If you show more interest in their life than their looks, you’ll stand apart from the “competition.” AND if they do start to open up a bit to you, LISTEN...and avoid interrupting them with your feelings. Let them talk.
Watch the signals. If they are quiet, don’t misinterpret the silence as disinterest or indifference. As long as they are continuing to listen as you go, this is a good sign. Even if they are not making much eye contact with you, they may be (believe it or not) shy, or afraid because of a past experience. Or both. If you are able to get their number, (or a FB friendship) send a creative IM or text messages that encourages them with friendly and creative words; referencing some of the things you already learned about them. This is better than the pushy approach, wanting another meeting right away.