1. DON'T. 

But seriously. Do you really think you're going to miss out on the love of your life if you refrain from hitting on that cute girl at the bar because this is your only opportunity to be happy forever? Just leave a girl in peace.

2. Don't be a dirt-bag. 

If you MUST—absolutely follow these pointers to make your best effort to not be a dirtbag. None of the following points matter if you're going to be a douche about it. Even the "right" things get ruined if you're whiny and can't take rejection well. *

*Note: I am a woman and interested in men, and I am playing on common societal stereotypes of overly-aggressive or clueless men hitting on women at bars, so I am using feminine/ masculine pronouns. Please feel free to replace with whatever pronouns make sense for you. "Don't be a dick" is good advice in general, regardless of who you are and who you're interested in.

3. BEFORE you hit on her. 

Successfully hitting on someone means expressing your interest while deliberately making sure the subject of your interest feels absolutely safe. This means if she's equally enthusiastically into being engaged with—yay! And if not—you leave.

4. Observe her body language BEFORE you approach.

Is she looking around the bar/bookstore/coffee shop, or engrossed in something else? Does she seem like she's waiting for someone already? Does it seem like she WANTS to talk to anyone?

5. Seek a NATURAL beginning. 

For example, if she's reading a book by your favorite author,* or you're both laughing at the same HIMYM episode playing on the bar TVs, or you both arrive at the venue soaking wet from a sudden rainstorm, a comment about the common interest or experience may be appropriate.

*(GENUINELY your favorite author. Don't pretend you like Tolstoy or McKinley if you've never read them.)

6. Pet names. 

Please for the love of all that's good, do not use a pet name.

7. Appropriate compliments. 

Do NOT compliment her on the way she looks. If you must compliment her, do it on something she chose, not something she was born with. Also "hey that dress is really cute"—although it's on something she chose to wear—could still be focusing on your attraction to her. Something like "Wow those steampunk goggles are awesome," or "I like your badass sword for slaying enemies" would be great.

8. Observe her body language DURING the exchange. 

Did she turn to face you when you began speaking, or did she face away? Clues you should let the interaction die at your opening comment: if her body is turned away from you (even if her face is toward you), if she smiles or laughs but does not respond verbally, if her arms are crossed or she exhibits other hesitant body languages. Unless she's blatantly interested*, leave. Better to err on the side of missing a cool encounter than err on the side of her asking for help from the bartender. Right? Right. Unless you're a douche.

If you're not great at reading body language and nonverbal signals, I strongly suggest you spend time on Google (or at the library) and ask for feedback from your friends.

*Blatant interest: turning her entire body toward you, responding verbally to your comment, and continuing the conversation. "Oh but maybe she's crossing her arms because she's cold—oh but maybe she's turned away from me just because she wants to get a beer from the bartender—oh maybe—oh maybe—" Nope. Don't want to hear it. Again: better to err on the side of caution.

9. End sooner rather than later.

If you've made a pleasant connection, wrap things up. She didn't come out tonight to meet you. Presumably, she has other things going on. Better to leave with someone wanting more than leave with them wishing you'd left earlier.

10. Give her an easy out--AND MEAN IT.

Examples of easy-outs may include:
ASKING if she wants to continue talking or not, with a totally neutrally offered option that includes you leaving her alone: "I'm enjoying this conversation, but if you'd rather wrap things up or have somewhere else to be, I'm also happy to do that. Would you prefer to wrap things up?" If you use direct language like "do you want me to leave you alone?" she may not feel as safe saying yes because she may be worried you would respond poorly to the potentially negative "leave me alone"—even if you were the one who offered it. Use positive and indirect language like "would you prefer, would you like," etc, so if she wants to stop talking, she feels very safe simply saying, "Yes, I'd prefer that."

Or, give her your number rather than put her on the spot by asking for hers.

Or if you do ask for her number, explicitly say: "It's totally fine if you'd rather not, or if you put in a fake number instead."

11. Wrapping up.

Personally, I almost never want a strange guy to hit on me. And if I see someone I want to talk to, I feel very comfortable being the one to start the conversation. With current societal dynamics, it seems much more safe and acceptable for women to start the conversation rather than men.

However, I have multiple female friends who express they enjoy meeting new people and being approached by guys, as long as it's done respectfully and safely. If you want to approach strangers, by following these tips, you'll be a long way toward ensuring those interactions are pleasant for EVERYONE involved.