That helps, but what a socially-adept person is usually looking for is for you to make a statement that relates their answer back to yourself and then gives them an opportunity to follow up:

  A: What is your major?
  B: English
  A: Oh, cool, I took an English course in college.  Probably nowhere near as detailed
   as your studies, but I enjoyed it.
  B: Oh?  Which course?
  A: Science fiction.
  B: Never took that one.  Which books did you read?
  A: A bunch of Heinlein, some Ursula LeGuin.
  B: I never liked Heinlein - thought he was a sexist pig.  I love LeGuin though.

The problem with asking a lot of questions is that there's unequal emotional investment between a question and an answer: the answerer is putting themselves out there a lot more than the questioner. (This is one reason why he who asks the questions controls the conversation.) If you're trying to build a relationship, this feels very awkward. Instead, the point of most conversations is to find & build a connection between the two people, one that lets both of them feel safe simply volunteering information and knowing that the other person is interested. By relating topics back to yourself, you a.) give both parties a chance to ask questions, and b.) show that you're in the same boat as them, and so they can feel free to open up to you.

Notice that conversations between close friends rarely have questions - they consist of people taking turns volunteering new information, often rather animatedly if they have good rapport with each other. Also look at Hacker News comment threads: people rarely ask direct questions, they just contribute additional information along the same lines as the original comment.