How to have a decent conversation with someone you barely know?

I’m usually shy when I meet new people and do not know what to talk about because I don’t know them. With time, I usually adapt my sense of humor, maturity, and what I talk about with a person. But the stages of meeting someone new and finding new things about them are awkward.

I want to know your methods because there’s a cute girl that sits next to me in science class that I don’t know that well and we only briefly talk to each other for assignments in short-lived conversations, then we awkwardly sit in silence.