It may sound old fashioned but i say a woman should never ask a guy out- if she wants it to last. If it is just a date -or something less serious- you are looking for, then by all means men love attention as much as women do (although they will deny that fully).
BUT if you are truly interested in learning more about this person and think it has a chance for romance then wait for him to ask you out. That said, flirting never hurts, and no need to be too subtle. Be careful though, there is a fine line between flirting and what some others have suggested!
Good luck! Let us know how it goes.
P.S. i have been here 2 years now and have been asked out by Swiss men. Its not every weekend, or as forward as in the US or UK, but it does happen!
Yes. Let him make the first move. If he's that interested, he will...
You also have to ask yourself, if you do it, would you be able to take being rejected if that was the case?
Find out what his hobbies and interests are. See if there is common ground anywhere. If there is, initiate casual conversations around this/these and see where that goes.
Don't fake it. For example, in pretending to like something he does. Too much wasted energy in doing that and sooner or later the pretence will become obvious.
Don't force it. Just be natural and yourself. If what you say by "we have been approaching for weeks" means there's some chemistry between the two of you, then that's a good sign.
Whatever course of action you decide on, good luck!
Laugh and point. Or is that what she's supposed to do? Or not do? Ah, hell. Just get up and do an impromptu interpretive dance to explain your feelings. If she's any kind of a woman at all, she'll completely get what you're trying to say. Remember, you have to do it naked. Bonus points for doing "The Helicopter".