If you don't know the girl (e.g., meeting a girl at a club or bar or on the street for the first time) here's a primer:

1) first, you have to get into a conversation with her. This is the hard part.
2) unfortunately, there are NO MAGIC WORDS that can start a conversation. It all depends on the situation.
3) some possible conversation starters include:
- Make a comment about something going on around you two (make sure you're not criticizing someone or boasting about yourself - choose a "neutral" or "positive" topic) If possible, be funny. If you can't, don't worry. Hopefully, she'll reply, and you can respond to that, and so on.
- Go ask her a question. This is probably the best way. Don't be shy. Be calm and smile. And I mean smile, not "leer" at her. Most girls will probably be fairly "surprised" to be asked a question by a stranger. Take advantage of this! Hopefully she'll respond well, and some conversation will start.
- If at a club or bar, you can buy her a drink. It might sound a little old and cliched, but remember most girls (and guys) are flattered by attention. Just make sure you're not leery or (too) drunk or unpresentable in some way.
4) After talking a bit, ASK for her number.
- It's as simple as that. Just ask her. Most girls will be flattered, maybe a bit shy, etc. Don't agonize about this part too much. Just ask in a FRIENDLY, calm manner.
5) Leave the scene of the crime!
- If you met her outside: make some excuse that you have to be on your way (she probably does too), and promise to "call her up". Alternatively, IF the conversation is going extremely well, and it looks like she has some time on her hands, you can ask her right there and then to "get some coffee".
- If you met her in a bar or club: This is a bit more tricky. I'll be straightfoward and honest: some guys will be having at least some thoughts (or hopes!) of a ONS with this "hot-girl-in-front-of-me".
This really depends on the girl. It's her choice. You have to be really good at judging character to tell whether she's into it. If you're having trouble getting her number, you're going to have trouble doing this. Also, having a ONS may ruin possibility of a longer-term relationship. And chance of rejection is much higher! Think of it this way: you already got her number, so it means she's at least reasonably into you. Don't throw that away. Personally, I think it's a bad idea (and dangerous to your health).
6) Call her
- Some guys agonize over the "right time" to call. If you call too soon, you may seem desperate. If you call too late, she may think you're not interested.
- My general guideline: call her later that night (if you met her during the day), or the next night (if you met her a night the day before). And I mean, CALL her - not some sissy text-messaging.
- Don't be nervous. Chances are, she'll be flattered that you're calling her, and she'll be quite shy herself too. Be friendly, and smile! (people can "hear" your smile when you talk on a phone).
7) Arrange to meet her.
- This time for a proper "date". Again, don't worry about planning some great romantic extravaganza. Keep it simple. A dinner together at a decent restautant will do. After dinner, a cafe or decent, snazzy bar is a good idea. Personally, I don't think it's wise to see a movie on a first date, because you can't talk to each other, and after the show is over, you can feel quite "dazed" after staring at a screen for 120 mins - not good for conversation.
8. Escort her home!
- or at least until she steps into the bus/MRT/taxi. Pay her taxi fare, if you can.
9) After that you're on your own!
Remember: Don't be discouraged by rejection! Don't be afriad of rejection!! Out of 10 girls you approach, most will end in failure. Suck it up - you're a guy. "What doesn't kill you, only makes you stronger"*. Practice, practice. The best way to overcome shyness, is to DO IT.
*taken from Nietsche