First don't act desperate and obviously don't tell her this. She will run for the hills. It's never easy to sell someone how you feel about them. Take this very slowly and try not to work yourself up to much.
Tell her that you like her. See how she reacts to this. Find out if she likes the same things as you do.
Is she seeing someone else? How would you feel about this?
The harder you try to get closer to her, the more likely she will reject you. Don't try to convince her, just let her make her own make up her own mind about you.
If you let your emotions get the better of you, you can create a situation in which a whole of emotional drama, pain and embarresment will occur. I am not sure what else to say other than just be real with yourself and her.