How do I find out if a girl likes me, or wants to get to know me better?

Ask her to hang out. Remember that the worse than can happen is she says no, and trust me, you will survive! However chances are she will, and you can use that time to get to know her, and see if you get any vibes. If she is an outdoors girl, ask her to go for a walk or skating or something, if she's not then ask her to do something she's interested in. If you appeal to her interests, chances are she will say yes, and you can build on that.

Flirt with her in simple ways that won't make either person uncomfortable... tell her a joke, give her a compliment, hold a door open for her... little things like that, and see how she reacts.

you should try talking to more people and build up your confidence when you are talking to people. it takes a bit of time but you will eventually get to a point where you aren't shy. like me, I'm not shy anymore but soemtimes I can be

If you're shy try something simple like smiling at her when you catch each others eyes or maybe greeting her with a friendly hello and/or wave when you see her. If she likes you this will either make her blush or encourage her, either cases are good as the blush is a telltale sign of someone liking you and the smile will encourage her to make the first move or show more obvious signs if she's confident.

I'd say if she actually speaks to you - you're off to a good start :) If you want to know if she's interested in you as more than friends - try asking her out! Dinner/movie is good. If you don't know her very well - try to get to know her better. Hang around her more in a group setting. Good luck with your lady!

Your seem to be in the same boat I was in, and her is my leg of advice. Ask her to a friendly event, not a date, something just as friends, maybe ask her to bring some of her friends and you can bring some of yours to lighten the tension. Hope this helps

There always other girls around you, so why the fear of rejection ?