Start a conversation with a girl?

Depends on where you are. If you are in a store you could ask her if she knows where something is, or something similar to that depending on where you are. Just act really friendly (maybe even a LITTLE flirty) and try to keep her talking. If she has time and finds you interesting. (funny, kind, friendly ect.) she will probably be more then happy to keep talking to you. If things go well, you talk for awhile, and you like her (it would work best if you find a large common interest) try asking for her number.
If you don't get it, don't be to upset. It you do, call her the next day. I would suggest not talking for to long, and then getting off telling her she can call you anytime the next day. If she doesn't call her back in a few days. (just in case she was busy that day) still, she will probably call her if she gave you her number and answered your call. (if she doesn't answer don't call her repeadly. That is annoying. Wait for her.)

"a girl who is unknown to us" hahahh, I'm sorry that's hilarious, like these girls are aliens

okay, so who are these girls. where are they, what's the situation? if you're in a bookstore, you can act like you're trying to find a book beside her and ask her a question "have you read __" something along the lines of that. and how she responds you take it from there.

i need to know the situation before I can give you advice on how to talk to these girls ;)

That would depend on what situation I'm in. I would just play it cool and not "go in for the kill" with them. I try to find something funny about whatever situation I'm in or something that I notice that draws my interest or just an observation - like if I'm at a club or the grocery store or wherever. Like, say I'm in a club & it's crowded. I may say something like, "Man, it's crowded in here tonight!" or "I think somebody should have alerted us of the impending stampede!" Usually, I like to make girls laugh, so, like if I'm at a grocery store and I'm coming around the corner and almost run into her, I will say something like, "They really should put traffic lights in this place!" I also like to make funny little comments about food at the store, such as, "I know if I eat that, I'll have to jog ten miles just to work it off!" I have gotten a lot of chuckles from women through making casual but funny conversation that way. Also, it helps to drop their guard when you use humor. However, I would suggest being real and not trying too hard or not giving them the impression that you're trying to pick them up. You're just having a conversation, that's all. So, if you give them the idea that it's just conversation and that nothing else needs to come from it but that you are just enjoying the conversation and keeping it loose, they will probably feel comfortable conversing with you. Another good website to check out is David DeAngelo's website. He uses the technique called being "cocky and funny" when it comes to meeting women. Good luck dude!

Never ever use a pickup line. Look at it this way. A girl would be used to hearing those. The moment most girls hear a pickup they either put their guard up or think ok game on, he wants me, let the games begin. If she's nice, just the same she will make you go through hoops.

What you do is open with something innocuous just as what any other pick up artist would do. Last night I was at a social gathering of professionals in my field of work and there was a pair of girls trying to order drinks. Looked at them and thought hmm how to approach and it went like this:

Me: "Hey I have never heard or seen your company logo, are you guys new?"
[pointing at the logo on their shirts. and note the important aspect, I called them *guys*, not girls or babes] and that lowers their guard down. I am just a guy curious about the logo on their shirt.

You might thing at this point and say, what if they don't want to answer? Well if they don't want to answer this, would they respond to a pickup line?

Girl1: No we're new

Me: "Oh I see, well welcome to the socials, maybe I will see you again sometime, damn I'm thirsty."

[see here I show that I am not so much interested in them] and I pretend to turn towards the barman. But halfway through. add "Ohh but what do you guys do exactly?" -- see I never meant to leave really. Just to show no real interest.

Girl1: yada yada yada . [ I don't realy care]

Girl1 has been doing most of the talking so far , she seems to be the dominant between the two, so I go to Girl2 and say

Me: So is she your boss? She seems to be the one doing the talking for both of you and I say it in a playful joking manner.

Girl2: No No, we work in different departments. blah blah blah [don't really care]

To cut it short, we ended up talking about how they both met, and what their future plans are which paved the way for me to pretend to try to read the palms of their hands [Learn palm reading trick. nice trick to play on a girl and she'll let you hold her hands and she'll get used to you touching her immediately] but then my buddies started looking at what I was doing from a distance and the girl I am dating is right next to them facing the opposite direction so I had to say bye.

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You see, you don't say a pick up line, you must build rapport, try to converse and start with something that makes you look like you don't really care about them being girls. or at least don't care about them being hot babes.

This will disarm them and let you in so you can dazzle them with your jokes, stories, comments. And let you show them that you can give them a good time.
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How about that instead of the usual "Hey girl, you look soo beautiful. Can I buy you a drink?" [This might work only if you are the best looking, most popular guy in town where all girls want you. Even then, they'd be enticed to play hard to get. :) ]

Search for "Pick Up Artist" on google, and also get the book "The Game" by Neill Strauss.

Good Luck!