Once I played in my mind what to say to a girl I liked in a language class over and over again, but when I saw her, I didn't say anything but "hi, how are you?".

I think being spontaneous and genuine have a lot to do with it, beside not expecting anything. Making mistakes and being rejected are also inevitable. I also agree that we attract people as we are, not as we want.

I suffer from a similar challenge, but I know it's my own flaw. I get anxious, and I fear rejection, and my mind goes blank and I don't know what to say. Girls though expect me to approach them, and to offer them something, as simple as making them laugh, for example.

It's the way it's that men have to impress women. Of course, after the first impression other qualities follow if you're serious. For example, education and personality. But the first impression (look-wise like you're trimmed and clean, and character-wise like confidence and sense of humor), and the first move are important.