I like a very very shy guy, and I cant tell if he hates me or not?

Okay, there is this guy, I have known him for a bit now, we had one class together last fall and he would not talk to me at all. We had to work together once for some project, and he would not look my direction or say a word.I just assumed he didn't like me, and at that time I didn't really care.
Then A little while latter he showed up at some event I was at and we talked for a very long time. But after that he again didn't talk to me until one day he sat next to me with a group of our friends and we talked, like normal people for about 5 minuets until I had to leave.
This semester we have another class together, and for some reason when I walked into that class I felt attracted to him. I waved to him and he waved back, but when I tried to make conversation he wont look at me at all, He talks with me for just a bit ( I start every conversation) but then stops talking after a few minuets if I don't keep it going.
I have a hard time making eye contact with anyone so I have no idea what he would do if we did, but i have noticed out of the corner of my eye he is sometimes staring at me and I have made him laugh before, but today I sat next to him and neither of us said a word. So I just don't know, some days he talks to me, most days he ignores me. I just cant tell what he is thinking. What do you think and how is the best way to try to flirt with him?
Thanks!