[header] How to impress a girl who's way out of your league [title] Be a gentleman. [step] Don't pretend to be jerk so that you can impress her. Both lying about your true self and being rude will put distance between you and the girl. 
[substeps] However, don't be afraid to tease her a bit. Once you've talked a few times, most girls will be comfortable with you making a few lighthearted jokes at her expense (as long as it's a two way street and she can do the same to you).