The first step of Swedish dating is don't be shy. Girls, if you're waiting around for that hot guy from class to ask you out, chances are that he won't. And it's not because he's not into you - it's because of gender equality. In Sweden, there is no reason why the girl shouldn't make the first move.
But remember, the same thing applies for guys. If you like a Swedish girl, just go for it and ask her out. Regardless of gender, it's worth making the first move when trying to date a Swede - because they probably won't.