Definitely in school (if you're in it... not hanging around... that would be a bit creepy in my opinion), library, park, etc. as all of the girls have stated.
In approaching, go up to the girl (hopefully she is alone) and make conversation about ex.:
Library: (sit next to her, stand next to her, go up to her), ask about a book she recommends, what is she reading, is it good? Then continue the conversation as any normal person.
Park: Nice place to hang out in the park, nice day, comment on the weather, about the town/city, etc.
Coffe shop: Do you know the area, what drinks do you recommend, where you from... sound casual. Hopefully you don't scare the girl. There is a chance, especially if she is not into you. But I found that if the girl gives you a chance (as I have) then it will work out fine. If she is really busy and moody, chances are she will think you're a creep and ignore you.
Well, I met my boyfriend at work... I did not talk to him at first. I thought he was weird as he was very friendly and talkative while I'm the opposite of him. lol But when he looked at my food (when we had lunch together in the office), he made a comment about it and we got on a conversation about food, where we're from, etc. and I opened up... still thought he was weird though but he continued doing that every time we had lunch together. Finally we exchanged numbers (rather, he got my cell and put his number on my cell... I was bored and decided to text him- which is how he got my number) and that's how it kicked off.