How do I approach this girl that I like?

Tell her hiiii. Then she will be like OH hiii. Then ask her how was your day and tell her your day and that is how you start a conversation

Here are some tips
(1) Pick a neutral subject. Since are in the same class ask what she thinks of the teacher, the material, the assignments etc. This a 'opening' topic because it something that both of you can relate to.
(2) Do know what kind of hobbies she is into? - Discretly overhear her conversations between other people in the class and see if you can figure out what she likes to do. She is outgong and really inclusive of other people, then quickly interrupt the conversation and add a comment. For example, say she likes snowboarding and she is talking about how she fell really badly or something, jump and be like, "I've never tired snow boarding, but I am thinking about it. How do you choose the right board. Blah blah. " that will get her talking.
(3) I don't know if you do presentations in the is class at school. But if you do let her know that you really liked her presentation (point out something specific). If she says 'thanks' and tries to keep the convo going. Then yeah, she is really interested.

It's hard to judge with what is going on since we don't really have an idea of what this girl's personality is like. Either way, I hope your risk pays off :)

I was shy until like. 3 week ago. And now I just seem to talk to girls and get a convo going very easily.

First of all you need to practice. Adults are a great way (your age is listed as under 18 so I'm assuming most of your friends aren't adults). Adults generally know how to keep a conversation going and will help you out if you get stuck (even if they don't understand that your practicing). If your ever at a formal party don't just sit back in the corner actually talk to the adults and see if you can keep a conversation going.

Second of all, when I talk to a girl ill make a broad statement that is generally agreeable. Something along the lines of. "Wow, this assignment is pointless. " Or if your school uses the "block" system of classes you could say "Whats the next Class/ block". Then when she answers be like "YES. English" (or "Ugghh. History") then turn twords her and be like "Who do you have for [class]". Now if she's talkative she will probably respond with a comment about her teacher eg. "Mr. Morlock, Who. " which you can use that to build off of. But if she's the kind for 1 word answers follow up with "What are you going over in [class]? " make a comment about what she says. If she goes "were going over WWII" just say what you think about WWII eg "WWII is so interesting, I love how the Italians got completely shafted. " That should keep the convo going for a little longer.
If your the kind who knows tons of trivia about lots of topics bring it up. Drop them in conversations. Throw them in to keep it lively.

Now I must say: someone before me said "ask lots of questions" I'm actually going to have to disagree with that. Asking questions is only good when the other person doesn't talk. That way it forces them to talk. But if the other person is generally approachable asking questions makes it seem like your getting to know them and they don't know you. It makes it seem less mutual. A lot of people will tell you to ask lots of questions but that's not the best way to keep a conversation going. Instead talk about yourself. Talk about things around you. MAKE COMMENTS ABOUT THINGS THAT SHE CAN RESPOND TO MAKE STATEMENTS THAT YOU CAN DISCUSS.

The one thing that people don't seem to understand is that people LIKE to hear about other people. You are an interesting person, talk about yourself. Don't overdo it though. Don't go "ME, me me me me me me me". After you have established a general conversational relationship with her go up and say something that happened to you that's interesting. "So I went to the mall yesterday and saw one of those iPhones. ". Talk about things that you like at first and then see if you can find out what she likes as well.

Make sure to ask her this how is your day that works with because then if she has a problem then you can ask her if you can help in a way.

Start with class stuff and ask a lot of questions. Asking questions is great, it keeps the pressure off you and most people like when people are interested in them (how often in the day to day are we really asked about ourselves? ).