How does dating work for the Modern Orthodox?

Throwaway account for obvious reasons but – seriously, how? I’m Jewish, but I was raised almost completely secularly. I was bar mitzvah of course, but that was pretty much the last time I went to temple. There’s a modern orthodox woman in one of my law school courses that I’d like to ask out, but I don’t know if that’s even permissible. To put in perspective just how assimilated I am, I didn’t even know that the prohibition on touching was called shomer negiah until I looked it up.

I’m by no means opposed to getting more religious, and I know that if this were to go anywhere that’d be necessary. But I frankly don’t even know where to start. Is just asking her out alright? What should I know but don’t? Actually, let me rephrase. Aside from shomer negiah, I know fuck-all, what should I know?

Thanks in advance.