Every woman I ever dated I approached completely out of nowhere.
From about the time I was 17 or so I was consistently getting anywhere between 2-3 numbers a week. Most of the time I wouldn't call just due to having a busy schedule or not really having hit it off with the woman.
I don't really mean to paint myself as a "Casanova" or anything, I actually was extremely conservative with the whole relationship thing because from the time I went away to college, I was already looking for "the one" rather than just trying to hook up or date.
For me, being a professional musician really helped out with the ease of meeting women and easily obtaining dates if I wanted. I say this mainly because it made so many things easier when approaching women ... for example: throughout college I worked at a dinner theater Thursday, Friday, and Saturday nights playing in the pit orchestra. The dress code was white bow tie tuxedo. At least for me, being at gigs where I'm wearing a tailored suit or tuxedo gave me a bit more confidence because I knew I looked good, especially when the venue didn't necessarily mean the audience needed formal attire ... aka I was better dressed than 90% of the guys in the room if I decided to stroll out and mingle during intermissions. The shows themselves gave at least a good opening line for small talk. I'd simply be able to ask, "how are you enjoying the show this evening?" and who knows where that would go. Sometimes we'd end up striking up a convo about the city, about the show, about television, about music, museums, etc... and half of the time, when the curtain dropped at the end and applause died down, there would be the woman I hit it off with coming up to the stage and looking down into the pit, waiting for me to come up the stairs, just for her to give me her number before she left with her party or whatever.
Sometimes I'd go out with two of my fellow musicians after a performance (still in tuxedo) and just have some appetizers at a local bar. Brian was in a relationship the entire time I was an undergrad (when I knew him) and Brendan was a little too timid to be much of a wingman, but eh, he still got a kick out of how I'd have no hesitation to walk up to a stunning woman at the bar and strike up a conversation. I often abstained from buying them drinks, it's too cliche really. I'd say a good 80% of the time they were completely uninteresting and I'd leave on my own and rejoin my friends, but there were times I started to hit it off.
Going up to a group of women is a little different, especially if you're not used to doing it. I developed a few "tricks" that I used over the years. One thing I'd recommend is getting good at performing a magic trick. When I say good, I mean really good ... like you're a professional illusionist with just that one trick. It really breaks the ice and often impresses the whole group of them because it's unique and jeeze, when is the last time a guy had the balls to go up to any group that any of the women have ever been in and perform a magic trick? If they ask for more, just be modest and say that you don't want to wow them too much, or something like that. The next thing I'd recommend is to start isolating the group into the "target girl" and one of her friends and just start with casual smalltalk like where they're from, how long they've known each other, stuff they do for fun, is it somebody's birthday, etc... and then eventually just use some body language to really hit home that you're into the one you're going for.
Best case, you'll have successfully gotten a date with your girl and have managed to pull it off with her group of friends right there, which will probably score some bonus points, just because they'll remember you and tease her later that night with stuff like "so are you going to go out with THAT GUY" or whatever. And worst case is that the one you fancied, or even none of them turned out to be that cool, you didn't get a vibe from any of them, got no number, and had to bow out to get back to your friends after an awkward minute or two of talking after doing the magic trick.
That's at least some of my experiences while I was doing the whole go out and meet women / dating thing. I'm currently engaged and have been in this relationship for a few years, so there's not much randomly approaching women anymore. Sometimes Debra and I will go to college parties (she's a college senior) and I'll just start talking to random people though. Like just last week for Halloween we went to a party where I knew hardly anybody, but if you're willing to just put yourself out there (and have done it enough to get past the nerves bit), you'll end up winning a few games of beer pong and practically giving a seminar to half of the entire party on Doctor Who to educate the kids who don't know what your costume is.
If there was anything I had to say for people who want to start getting up the "balls" to approach women they find attractive, it's this: practice makes perfect. Just like the best way to get over stage fright as a musician is to just keep playing for people and bigger and bigger audiences ... eventually it's no big deal to be giving solo recitals or playing the opening trumpet call of Mahler 5 for a packed 5,000 seat concert hall. Worst case you're going to strike out, and that'll happen a lot just because, to be honest, you're not going to hit it off with everybody anyway, so you don't know the girl from Eve, what's to say she's even your type personality wise ... exactly, so just go for it and whatever, eventually you'll figure out the right balance of tact and directness to get results.
