I'm just a college student studying in Europe for the term, so I'm not quite as experienced in giving dating tips as most people are, but here is my two cents.
I've been noticing that all the American girls abroad are falling for European men, while all the American guys are failing miserably with European girls.
What I've realized in my observations and interactions with Europeans is that European men have to try much harder to get girls from their respective countries, while American men can be more relaxed in their approach with American women and be equally successful.
So... get some American girls with European men and the girls become spellbound.
I noticed that Europeans in general tend to converse with complete eye contact, even in casual conversations. At first it feels weird to be staring into another person's eyes, especially with casual conversations. But once you get used to doing so, it's very easy to do hitting on a woman.
Also, Europeans seem to expect that much eye contact, so anything less will be a failure on the man's part.
The Europeans don't even have to be funny. But equipped with good eye contact, which exudes a certain feeling of confidence, it's very easy to get a girl to feel attracted to you.
Also, keeping that eye contact will allow you to notice many subtle responses in her face that you would have missed when darting your eyes around the room. Big pupils are a plus.
Once your eyes get distracted, she will be distracted. And if she's really hot, as soon as you look down, there will be another guy coming along to swoop in for the kill.
Practice makes perfect as always.