Exactly same way you'd approach any girl.  Smile, say hi, and start a conversation with her.

Walk up to her (preferably from behind), hit her over the head with your club (not too hard as to cause the head to collapse, hard to have a conversation with a corpse) and drag her by her hair back to your cave.

It may be old school, but that is how I roll.

Personally, I prefer the snare in the park.  Just put an ipad or a "hello kitty" as bait. When she steps in the snare:"Gotcha!"
I tried the club like Xpat John suggested. All she did was take it away from me and spent the rest of the afternoon playing "Sammy Sosa" with ME as the ball!

Well, this is the five thousand year old ancient Chinese technique, which can be seen wherever young people in China court:

1) First, get really big girl hair, if you are a guy. The bigger the better.
2) Practiced depressed-looking poses in a mirror. Try to imagine a puppy getting hit by a car, and see how sad you would look. Try to look that sad all the time, always look downwards. If the puppy thing doesn't work, try screaming "I... SO SAD" and you might fool her.
3) Try wooing her with some lines like "I GREATEST MAN EVER LIVE!! MOST HANDSOME MOST BEST MOST STRONG MOST CLEVER MOST HUMBLE." I assume Chinese chicks dig that because it's the main tact Chinese guys use.

If this is a girl you already know, then I would suggest a funny joke to break the ice, and then invite her to dinner.
If you want to meet girls, then head down to the local disco and sit alone with many beers on your table.  You would be suprised how well this works!! 

From the front
I lived in Thailand long enough to be wary.

If you know how to call a kitty or dog and use food , to help call the critter. This is a good technique,same works on girls, talk the same soft tones, stand slightly bent over so not appearing treatening, and call to the girl to come here, only use Maos for bait.

best to do this on a bus. take your left hand and place on her left breast (outside the shirt) when she looks at you say "ipad"

Just say hi how are you in Cantonese or Mandarin

You guys are all missing it.. The best way to approach a girl is:

You need to put yourself into situations that you can easily strike up a conversation.
1. Go to a grocery store is a good place. Men are to know nothing about food products or how to cook or how to shop or (if you are a western) read the labels on the products or don't nothing about freshness or where to find anything in a grocery store, etc. Here are several ideas to help you to strike up a conversation because you are poor helpless man.  A grocery store, also allow the woman to look into your shopping cart to see what types of items you are buying. If the cart is filled with packages of soup noodles and bread, we will thing you are single but if it is filled with woman's hygiene products or diapers, she know your married or have a girlfriend.
2. Go to places like Starbucks where it is quiet. The successful rate in a coffee shop is generally much higher than it is in a bar. It is much more respectable to say you met each other in a Starbucks than you picked her up in a bar. Personal, I don't chase the women, never have but I have had several women try picking me up in a Starbucks or coffee shop, especially in China. You just sit there alone. There are many opportunities to either start a conversation or give a woman a look and a smile to attract their attention.
3. If you are a Chinese guy, join an evening English class. Many Chinese girls love learning new languages and most of them are single. I am almost sure these girl join these classes to meet guys or because they are single and they have nothing else to do with their time. Talking about opportunities to get into a conversation with a girl, this place is a gold mined.
4. Travel on the subway and be very observant of your surroundings. If you are a foreigner, many of the girls will give you signs that they speak English. When they see you, they will open an English book they have in the purse or call a friend and speak English to them or will use one of those electronic English dictionaries. Watch them carefully, you will see that they are actually showing you intentionally. Again, a great place to start up a conversation.
*NOTE* once you find the girl and you do have that converstaion, be sure to get their number or find a clever way to give them you number BUT don't do what some guys do, don't give them a business card with your photo on the front of it, which I call a "calling card". Come on guys, the girls can see playboy and player written all over that idea.