If you've got a crush on a shy girl, it can be hard to approach her at first. So just take little steps. Don't ask her out right away. Instead, start by saying "hi" on a regular basis. Whenever you pass each other in the hallway, make eye contact (this might be hard) and smile. Use her name, and greet her in a friendly way. Friend her on Facebook, or other social networking sites, to learn more about your crush. Talk to her friends to find out if she's dating anyone, or what kind of people she likes to date. Try to learn about her hobbies, how she spends her free time. Learn what she likes.  Often, shy people will feel more comfortable talking online, or texting. Becoming online friends first is a great way to get to know a shy girl.  Don't assume girls who act shy around you like you, or don't like you. Shyness isn't a sign of anything except being shy. If you want to date, you need to do more than say "Hi" and scamper off. Once you feel like she's comfortable enough with you saying hi to approach her, just walk up to her some time and have a short conversation. Make sure she knows who you are before you ask her if she wants to date. Keep it simple: "Hey, my name is _____, we have Biology class together." Shy people are often quite good at one-on-one conversations but struggle in big groups. Don't try to engage a shy girl in class, or while you've got four of your friends with you, or it's going to be rough. Bring up something simple to talk about, something that you know you have in common, and have a short one-on-one conversation.  If you're in class together, just talk about class: "I really messed up that last test. It was so hard. How'd you do? Do you like this class?" You could also arrange to talk one-on-one at a later time. For example, you could say something like, “Hey, do you have a minute to talk right after school gets out? I have a question to ask you.” Lots of shy people fear that they're "bad" at having conversations, and don't like to talk because they're afraid of messing it up or being awkward. This usually makes it worse. Instead of drawing it out, just exchange a short little chat and then break it off. Say, "Hey, good talking to you. See you later!" If it seems like she feels uncomfortable, don't draw extra attention to it. Just end the conversation in a friendly way, with a small compliment. "It's so good talking to you. You're funny. Let's talk again soon." Keep talking to this girl. Have your little conversations, making them gradually longer and longer. When you start to feel comfortable talking with her, just ask her out.  Keep it simple and keep it short: "Hey, I've always noticed you and I think you're a really sweet and really nice person. I like you a lot. Would you like to go out with me sometime?" Sometimes, things like dances or other big events can be intimidating for shy girls. It's actually sometimes better to just keep it vague: "Would you like to go out sometime" might be better than, "How about this Friday?" You can also ask her if she would prefer a social event or something quieter. For example, you could ask if she’d prefer to go to an upcoming dance, or just go to a coffee shop and talk.
Start by saying hello regularly. Find out a little more about her. Introduce yourself. Talk one-on-one. Keep your talk brief. Ask her out in a simple way.