What should I do to show her I'm interested?

I think the no-pressure rule should apply here: ask her if she would want to go out for coffee or lunch after class (have you had lunch yet? Wanna go get something? ) and see what develops from there. She will give you signals, only if you give them out too! Try to talk about things outside of school, (How was your weekend? Oh yeh, sounds exciting! I did X,Y,Z. You should come next time) but make that last remark sound very casual and friendly, if she's interested she'll enquire about going out again and try and invite herself along. But I find that when guys (who are my friends) tell me outright that they like me, and I can't return their affections, it makes the friendship awkward because you can't just go back to the way things were and laugh and joke around, because you are constantly worried that they might take it the wrong way, are they reading into this etc.? My advice, just be friendly and casual, you will find out if she likes you or not! Good luck.

Is there any signs on her side that show that she may be interested in you as well? Just be honest with her. That's really the only thing you can do. Don't mess around girls hate that. If you really like her, tell her. It may be hard to work up the courage, but that's the only way you will get anywhere. Good luck!