(M20) What to do when I get flirtatious looks?

Hi folks, I'm 20, and most of the way through engineering school. I've been single for a while, and have recently gotten back into the gym, adopted a new haircut, and started dressing a little nicer (no more plain brown t-shirts and holey work jeans in class, I'm trying to wear a button down shirt, and presentable pants every time I go to campus. Most of the time I look like a farm boy in "Sunday best").

Either way, I'm doing something right. I've been noticing women on campus looking over at me in the library and in class/ the coffee shop. So my question is, what in the world do I do when someone is checking me out? All of my past relationships have developed out of close friendships. Never by meeting someone by accident on campus.

If it's worth anything, a little about me. I tend to be friendly, and out going. I can hold a conversation for atleast a little while about almost anything, with almost anyone, provided that they want to talk. I have a misguided sense of gentlemanly chivalry that leaves me all but incapable of "hitting on women". It may be behind the times, but it's deeply ingrained. So the pickup line thing may not be for me..

Thanks guys. I appreciate any advice. Or, have a laugh on me. Sunday best...This guy..

Edit: Thanks to everyone that offered advice! That all seems pretty common sense, and I have some idea of what to work on, and what to do now.