How to meet a guy?

I just started college and there's a class called technical drawing which I share with a few classmates and one of those classmates is a really cute guy. I have this class every Sunday and last Sunday before this one the teacher was kind of late and he came up to me and told me that the teacher may not come and give us today's lecture and just chatted for a little bit. We got a message through our phones saying that the lecture's location is moved to another location and when we went there there was some technical problems they had to finish before they got us in. As were waiting he kept peaking at me and I could see him looking at me like he wanted to tell me something but I was just too shy to go and talk to him I kept talking to my friend who was infront of me and waited for him to come and say hi. He eventually had to come and talk because his friend came to talk to me and he came in and started talking and laughing. Now this last Sunday when we were in class he was sitting in the front and I was sitting in the back , and he kept peaking at me and when I catch his eyes he turns around. I didn't know if he is interested or not until when everyone finished and handed their assignment in class, he handed his but I wasnt done with mine. I looked at him and he was examining the other assignments everyone else did but there was only 3 people left in class including me. I took way too long to finish mine so I think that's why he had to take off. He seemed quite interested in meeting me , but I have this fear that if I meet him that I'm gonna ruin the relationship sooner or later or that it's not gonna be as I expected.. I don't know how to take the first approach in having a good relationship that would make both of us happy? In short : how to take the first move in talking to him without being nervous?:))))