TAKE IT SLOW! It will be a few weeks or maybe months before you can 'approach her'.
The next time you saw this girl, go up to her and just say 'hi, how are you?' pleasantly. Every time you see her for a few weeks just smile and say hello, and have some short conversations with her - maybe about what you're both doing that weekend etc.
After a while, she should smile and say hello when she sees you. You've basically built up a minor friendship with her. That's a good starting point. If your interests are, say, going to the movies, talk about movies you've seen and discreetly find out what movies she likes. If your interests are a certain kind of book, let her see you carrying the kind of book you both like. Then start talking to her about it. She'll find out you have the same interests.
If you both like the same kinds of movies or foods, after about a month (any sooner and she might think you're manipulating her or using her) ask if she wants to go see a movie or eat out somewhere, or go shopping. Say she can invite her friends too and you should invite some of yours to avoid making her feel pressurised. She'll be more confident with her friends going too. THEY AREN'T DATES!!!
Do this a few times, then ask if she wants to go to a movie or something with you WITHOUT other friends. She should say yes. If she doesn't, don't make a big deal of it. Just smile and say 'some other time' and try again later. While there, DON'T pay for her ticket but DO buy a big bucket of popcorn to SHARE. You aren't going out YET!
Do this a couple of times too - then say something like 'I don't know how you feel, but I just want to tell you that I have always liked you. If you want, could we go on a date sometime?' Then say she doesn't have to decide right then. You should say it at the end of the date so she has time to go away and think and doesn't feel pressurised.
If she doesn't want to 'go steady' then stay as friends with her. You can always wait a few years to ask again. If she says yes, take that slow too. Just hold hands and go on dates at least once a fortnight. Don't take over her whole life or let her take over yours. After a time, try some kisses on the cheek or pecks on the lips. Don't go straight in for 'big' kisses - she could end up feeling cheap.
Main thing is to take it all SLOW...