Don't be so blunt. Don't just go up to her and be like "hey you wanna go out?" That freaks us girls out. Compliment her but not too much. If the compliment comes as a surprise to her she'll be awkward and won't know how to respond to it. Then it'll make an awkward moment in the conversation. Ask her simple questions like "How is your day going?" Or if she's looking down or frustrated just ask her if she's okay. Little things like that go a LONG way :)
Always be yourself to get people like you. Befriend the girl and try to find out how she is doing everyday. Be nice to her and to other people around her and let this be your personality. You may ask her out and spend some time with her, be there for her when she needs you.
Talk to her about something that she can talk about with you but both of you won't feel nervous.
You can say you like her shoes and ask her where she got them, then you can ask her what she likes better, "shopping by herself or shopping with friends or family" and then ask, "how come?". When I was very young, this is how a boy talked to me. Then he asked me, "If your friends liked it, would you wear your brother's clothes?" I laughed because he didn't know I don't have any brothers so then he asked, "If you had a brother, would you wear his clothes if your friends liked it?" We talked to each other for a long time and that's basically how I started to like him.