There really isn't an easy way when it comes to relationships. Although there is a smart approach to relationships, but that doesn't mean that it's easy.
So first of all, get to know this girl more. If you only have one class with her, take that opportunity to talk to her as much as you can. Even if she's always with a group of friends, you have to try to get to talk to her alone or maybe talk to her entire group as a whole. I know that you said you are shy but if you really want this girl to be your girlfriend, you have to be brave. You can talk to her about the class that you're both in, the homework and assignments in that class, gossip about other classmates that are in that class, or talk about the teacher. Pretty much anything can be used for small talk. It may seem awkward at first, but it can also be a nice way to get a conversation started. When initiating conversation with her, pretend that she isn't the girl that you like for a second and that she's one of your friends. Talk to her like you would talk to your friend. I know that it's easier said than done, but it takes practice.
Once you get to know her a bit more, you guys can start to be friends and hang out. During this stage, ask her questions about herself. It shows that you are interested in getting to know her and that would probably boost up her self-confidence. People like being around people who make them feel good, so remember to do that.
Then after knowing each other more, you can consider asking her out. When asking a girl out, try to do it in person. Don't do it through email, text, phone, or Facebook. It kind of makes you look lame and it makes it seem less personal and meaningful. You don't want that to happen so you'll have to be brave once more and ask her face to face. There really isn't all much I can tell you about that except to find courage in yourself and find motivation to do it.
If she says no, then you have to accept that and move on. She can't help the way she feels and you should respect her feelings. It'll show that you are mature and it'll also help you get over the rejection later on. If she says yes, then celebrate and throw a party but only in your head. When you're still in front of her, don't get all crazy. Act cool and simply smile at her. Then start asking her when she's available to go out. You'll both be feeling pretty giddy so I don't think that it'll matter so much of what you do and say after that point. Trust me, feeling giddy kind of screws your memory and your thinking process for a little while so you can get away with being awkward.
Dating someone isn't as easy as it sounds. It's actually hard work considering the commitment, all the overwhelming emotions that go with it like jealousy, paranoia, excitement, and so forth, as well as the overwhelming amount of thought such as thinking about her all the time. For one, you need to try to control those emotions and thoughts. They will only bother you and stress you out if you keep them around. Sometimes, it may actually ruin the relationship. So the "easiest" way to go around this is to try calming yourself down every once in a while. When you start to think too much about her and all these emotions start to surface, stop yourself and breathe normally. Think about other things and redirect your energy away from her. With practice, you'll be able to control them better and you won't end up going crazy. Seriously, these thoughts and emotions can literally drive you insane with mild to extreme mood swings and paranoia. I must say, that is not fun.
So anyway, I hope that this helps you out a little bit and I hope that you are able to ask her out soon. Like I said before, there really isn't an easy way in relationships. But with a smarter approach, you are far more likely to succeed than not. Good luck!
