First, the obvious questions: What do they do for a living? Where are they from? Establishing context (How they know the host of the party or what they are presenting at this conference or how do you know the person who just introduced you etc.)
Second, the social “sizing-up” that you do by observing how this person speaks, the words they use, whether they are funny, interesting, if they listen more or speak more etc. Do they speak well? What things do they reference in their conversations? Are these references interesting, useful or funny? This is perhaps the step that reflects the social class, the privilege this person has. This could also be where you look for commonalities: do they read the same books that you do or watch the same shows that you do? Did they love these books/shows or hate them?
Third, you have deeper conversations. This could be where you explore the differences. Why did they think the X show was bad or why they did not like the Y show you thought was good (because if they like the stuff you like too then you know the reasons)? Or maybe this person has an interesting job or life that you want to know more about. That is a step to probably ask them a few broad, big-picture questions, things that help you understand what kind of a person they are.
Now after this a lot of decisions are made: is this a potential friend? A nice person, a good person, a lovely person? Do you want to talk more and discuss even more movies, books, politics or big-picture topics like value systems or life experiences?