So I 'think' I like this girl... how should I approach her?

[Tiggey]

Be sweet, and don't come off as creepy. Firstly, play it cool. Don't compliment her too much (I think three compliments per conversation is the limit), and try to stay calm. Introduce yourself with a simple hello, and try to be cheery. Once you're past the greeting, slowly begin to ask about her interests. (It's best you do this if you can sit next to her, or get her alone somewhere. People are usually different around friends of the same gender.) Make sure you know how she talks, for example if you swear a lot and she doesn't, try not to swear too much. Some people find it off-putting.
The simplest way to find out if she has a boyfriend is to find her on Facebook (if she has one). Once you break the ice, ask if she has one. If she does and you don't know her last name, ask for it. She'll probably want to be your friend if she thinks you are nice, but don't expect her to be messaging you. I'm not sure about other people, but I don't like to be messaged as soon as I become friends with someone. Then again, I don't really like messaging at all. So, leave all the conversations for real life for a little while. Check her Facebook relationships, though some people will leave it single if they want privacy or if their significant other doesn't have a Facebook. Just to be sure about it, you can always wait until the topic comes up. Some girls are open about this, while others shy away from talking about it with guys. Don't immediately ask if she has a boyfriend, and this should be for obvious reasons. Just wait it out, and you'll probably be able to know once you become friends with her, rather than acquaintances. I would like to advise that these are simply my opinions, and with this topic it isn't one size fits all. Good luck!