What is the best way to start a conversation with a girl?

Okay, I'm a 15 year old girl so I can answer to help you lol
just be yourself, girls at that age really don't like guys that are all full of themselves and try to act cool. If you're yourself then they will think your sweet!
If your starting a chat at school, you could simply ask what they are taking subjects wise, teachers, work anything. If you don't want to talk about school or its a girl outside school ask about weekend activities and where they like to hang out?
BE YOURSELF! girls like that the most!

Well I'm 17 even though I have never had a problem with flirting I have had some bad experiences with guys who didn't know how 2 flirt. First off if you like some1 and you want them 2 know it try to catch that persons eye when you do smile or smirk at them and turn away or if ur anything like me make conversation with ur eyes just smirk a bit and think about everything you would like 2 say 2 them it comes across in ur eyes and they can tell it. After that check 4 signs 2 see if that person likes you like if you see that person looking at you or says things 2 you or try 2 make small talk, if they don't you should go up 2 them and just make small talk because that person may be shy. Don't play around with a lot of girls because you don't want 2 confuse the person you like by making them think ur just a big flirt, and NEVER EVER play around with a girl like non stop until the point that she doesent know when ur serious and when are not because if you really like that person ur going 2 need some serious time and you don't want that person 2 laugh the whole time or feel like they can't take you serious.

Disliking a teacher? That can be a good conversation starter. Maybe something to mention, just because you have it in common. But, don't dwell on negative. If you talk about anything at length, make sure it's fun and positive, and not too personal. You want to be a positive guy. I'm not a genius when it comes to girls, but positive people tend to have an edge in dating, relationships, and life in general. If anyone tells you I'm wrong, they probably hate everybody.

Hey man. I'm 22 years old from Philadelphia. Trust me when I say that all you need to do is keep the conversation going. If you can goof off and get her to goof off with you, your doing great. Just try to keep telling yourself this "Pay Attention". Women like to throw curve balls at you. Just go with them. As long as you keep the jokes coming, she'll stick around. Don't look away from her through, keep your focus on only her. You'll do good man. Check back in with me for more advice and also to let me know how that worked out. Just trust me, do as I told you. It works.

Find something to talk about, be it homework, sports if she has sports apparel on, if she dislikes a teacher, tell her she looks pretty and introduce yourself, etc. It takes practice.