How to Talk to a Woman

Gauge her interest with eye contact. Shoot her a quick gaze, wait until she notices, smile with your eyes, and then slowly look away. If you look back and notice her looking back to meet your eyes, she's likely interested in talking. If she completely avoids eye contact with you, she's probably not interested or is too busy or distracted to notice you.
If she's talking to another guy, back off, unless you're really feeling bold.
If she's with a group of girls, then your chances may be better if you go talk to her with a group of your own friends.

2
Get within talking distance. If she's looking at books, go look at books near her. If she's at the bar, go order a drink next to her. Find any excuse you can to casually bring yourself close to her. In some situations, though, this will be difficult (such as if she's absorbed in her laptop at a coffee shop, or talking with a friend). In that case, it's probably better not to interrupt her unless she seems obviously intrigued by you (i.e. she can't seem to stop looking at you).
Don't wait too long to talk to her. If she sees you looking at her and approaching, then let her see that you're a man of action, smile, and walk up to her.

3
Strike up a conversation. Keep it casual, as if you already know each other, but not too casual because you don't want to scare her off. You can start with a simple observation and end it with a question: "Nice day, isn't it?" or "This place sure is packed, huh?" What you say isn't important. You don't really need an answer to the question; you are simply inviting her to talk with you. If she responds pleasantly, continue the conversation. If she doesn't respond or seems preoccupied or disinterested, she probably isn't interested, so start talking to someone else.
Don't worry about saying the perfect thing at first. You just have to get the conversation started and can wow her later. Don't go for a pick up line or something that just doesn't sound like you.

4
Keep your conversation organic. Don't come in with “canned material”, “nuclear attraction” routines, or other social robotics. The best way to make a connection with someone is to come from the heart and live fully in the moment. What you say isn’t nearly as important as how you say it. Socializing is about exchanging energy, not being a wordsmith. When in doubt, just say “Hi”.[1]


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1
Compliment her. Since you just met, you shouldn't tell her she has the world's most beautiful eyes or that she has incredibly sexy legs. This will freak her out for sure. Instead, compliment her sweater, a piece of unusual jewelry that she's wearing, or even her laugh. You can maybe go as far as saying she has nice hair, but don't get much more personal than that, or it'll be too obvious that you're interested. Say something that you mean and which makes her genuinely feel appreciated.
Just one compliment during the first conversation is enough. You don't want her to feel like you're trying too hard.

2
Use your environment. If things are a little awkward, at first, you can look around and use your environment to guide you. If you're in a bar, say something simple like, "Do you come here a lot?" or "Have you tried the mango mojito? It's ridiculous." If there's a poster advertising a concert that's coming to town, you can ask her if she likes the band. If she's wearing a Cal hoodie, you can ask her if she went to Berkeley, because your sister did.
You shouldn't look around too much or the girl will feel ignored, but if you're nervous about what to say next, the environment can be a great help.

3
Master the small talk. There's nothing small about small talk, so don't skip it. Small talk is the stuff that can help you transition into the big topics, and you can't just go from "How are you?" to "What do you think is the meaning of life?" So, start off by talking about what you did over the weekend, the weather, your friends, your work, or whatever you think will keep the girl interested. Keep the banter going back and forth and see if you can make her laugh. Don't be too nervous about boring her; you're just getting the conversation going.
Make her feel comfortable about talking to you about the light topics, and soon, she'll be ready to open up a bit more.