It is always easier to talk about things rather than shooting the breeze. The more difficult the professor, the more concrete you want the things to be. You could:
- Wait until class has started and have a legitimate question (as Buffy mentioned above).
- Read some of his/her research. Figure what they're interested in. Talk to his/her grad students and ask them what they do. Find something they are really interested in. This is riskier since you might be truly ignorant about it, but asking a smart question about something the professor is truly interested in (i.e., not just the class) can score you major kudos.
I had one such (world-renowned) prof who taught one of my classes. I thought he might be interesting as an advisor. My dutch courage was to drink an entire pot of coffee before going in to talk to him about problems he brought up in class which I thought interesting. (Note he was both a smoker and coffee drinker so he appreciated zippy conversations). We spoke about topics in class (on Riemann Surfaces) and it was clear that because he brought them up, he was interested in most of them. At the same time he was known as not taking many students at all, and being both quick and gruff.
We did not ultimately pair up, but he seemed genuinely entertained by our encounter (smiling and sitting sideways in his chair) and we spoke for at least an hour about topics related to his class and areas for futher research.