Remember that women are people first. Have you looked at the mefi threads dealing with this topic? There are tons of them--including ones dealing with people from south Asian backgrounds.

A) It's not your groove that you're looking to get on, technically. It's important to be clear about this.
B) It sounds like you're coming from a Guess culture, and where you've moved, might be mostly an Ask culture.
C) Flirtatious looks are all well and good, but a good ear, reasonable empathy, and the simple grace of being clear in expressing your desires, are far more powerful and reliable means to your end, in almost any culture. Generally, you're going to have much better luck if you start conversations, ask women out socially, and be willing to be the initiator of relationships, than if you act at all coy.

Good luck. Ask a woman out, today.

I may be way off base here, but I believe that you may be the only practising Muslim posting here; to the best of my knowledge you are the first to proclaim yourself so, anyway. This sets up some potential equations that may be beyond the ken of the Metachat knowldge base. For example: do you wish to attract Muslim or non-Muslim women? If the latter, we may be of some assistance. If not, I don't know how much help we can be, given the cultural differences that may be in play.

Again, it's entirely possible that I'm incorrect in the assumptions I've made. More information on the sort of person you're interested in would probably be helpful.

Proceeding blindly: I don't think you can go too far wrong with the aforementioned smile and "flirtatious look", but eventually you will have to strike up a conversation of some sort. Being a shy person myself, this is indeed the hardest part of what we might as well call courtship.

Without knowing any of your particulars, my advice would be to ask your intended about herself - where is she from? If she's not originally from where you are now, how did she come to be there? etc. Draw her out from there.

The idea here is to keep the focus on her. You can drop in some of your own history where it seems appropriate, but the main idea is to express your interest in her. Listen to what she says, and respond accordingly. DO NOT try to fake an accord. It's either there or it's not.

After some sort of rapport is established, and when the conversation seems to wrapping up naturally, suggest meeting someplace very public - a cafe is always a good choice, but whatever the local equivalent might be would probably work - at a later date. (Allow at least three days interim, lest you seem too forward.) The idea is that you can continue learning about each other in a place that is neutral and unthreatening. At this meeting, feel free to be a little more forthcoming about your own circumstances, keeping in mind not to dominate conversation.

Should this meeting go well (as we all hope it will), perhaps you might proceed to a cultural event - film, concert, etc. Personally, I've preferred to save such an outing for a later date. I've always felt the the first date should be about establishing some sort of connection. Your mileage, of course, may vary.

Should things go exceedlingly well ...in the culture in which I grew up, it would not be remiss to offer a kiss at the end of the evening. If things went relatively well but are not fully clear, you may want to wait on this until the second date, should such an event occur.) This offer may or may not be recieved well. If not, DO NOT push the issue. Rather, chalk it up to experience and set your sights elsewhere. If, however, such an offer is recieved and reciprocated... enjoy your good fortune, be happy, and by all means proceed with caution.

Being non-Muslim myself, I am somewhat full of bourbon at the moment. Feel free to take any and all of what I've laid out with however much salt you require. I don't think I've steered you too far wrong in my somewhat rough guide to dating; at any rate, I certainly hope not.

Good luck. Don't expect to "hit one out of the park your first time at bat", if I may use a baseball metaphor, but don't discount the possibility either.

awww, you're my age and everything! I think you're adorable. I'd run after you if I were Muslim and weren't already taken.

Well you charm a lot of the ladies here, for one! Being nice, smart and curious about people is very grooveworthy. Honesty and openness about your feelings is also a major chick magnet.

Also, do you want to flirt? Western style or Muslim style? Or are you looking to get married? Or are you looking to date, Western style? I've got advice for you for all of these permutations.

In terms of the initial glance, tho, try to convey your shy sweetness with it. You won't be a borer or a leerer. You're more of the glance over the newspaper/wide open grin type.

Getting a big smile back is great!

If I were a Muslim guy looking to Islamically pick up chicks, I'd volunteer at the mosque/do study there with the fathers/brothers/uncles/etc of the girls I like. Then I'd try to get invited for dinner, at which I would cast shy smiles at the target girl. Of course you might be trying to do something else entirely..

Heh, I think I have a crush on By the Grace of God…:)

Thanks brujita and paulsc, but I think bmarkey nailed it (sorry for being so vague with my earlier question).
It wasn’t so much how to behave with women that I was inquiring about, as much as how I should go about getting through that first awkward stage where you think the girl likes you (she’s checking you out in the supermarket line, maybe?), and you’re not quite sure how to proceed; I mean, you just can’t go up to her and tell her that you think she’s cute, or can you (sexual harassment)?
Can you say “Hi, my name is so-and-so, and I was just wondering if you’d like to get a bite to eat sometime?” (I suppose so, but that sounds so mundane, and I was looking for something with a bit more zest to it.)

The only problem is, there’s no way of finding out if I’ll like the girl before hand so that in the event that I don’t find her personality meshing with mine, I won’t be left with a messy break up. Which begs the question—why should the break up have to be messy? I mean, I can not “love” the girl and still be friends with her, right?? (Not so sure of that one.)

It doesn’t matter if she’s a Muslim or not though, but it would be nice if we both believed in the same things.

Macho ≠ attractive to ladies (in my experience, or at least not always). Remember they are most likely looking for the same thing you are - a good conversation, fun, respect, sympathy, humor, all that. So yes, smiles and flirtatious looks are a good place to start, and if you feel the ocular invite well-received, strike up an honest conversation! Good luck!

Asking a stranger if they want a date or making a comment about her looks is coming on too strong. Start with "hi" and a neutral comment about the weather or your surroundings--if it's in the market line and she has the ingredients of a favorite dish, you can make a comment about how much you like it...bookstore or public transit and she has a something by an author you enjoy, say so...and so forth.

And yes, you can be friends with a woman to who you're not physically attracted.

And cheer up; you're 27 -- wait 'til you see what you're in for when you're trying this at 45!

You're starting the conversation because you like her. The conversation is either about HER or the ENVIRONMENT or both. Not about you or your perceptions (i.e. cuteness) of her looks. Curiosity and praise with a smile work well.

For example:

Good choice, the chicken soup here is good!
I can't believe how late this bus is.
Have you seen "Cats" before?
I thought what you said at that meeting yesterday was extremely helpful or interesting.