From the title, it doesn't take a genius to know where this form of discussion originates. Socrates used question based teaching as a mode for promoting higher level learning. What's good for the Greeks is good me.
The basis behind the concept of a Socratic Seminar is to create student led conversation. The meaning of a topic is analyzed, understood and retained due to direct individual involvement. Teachers, in a Socratic Seminar, must allow the process and it's participants to carry the activity.
Here's how I managed a Socratic Seminar. Arrange student/s seats in a circle(s) facing one another. Obviously the size of your class can alter the dynamic/s of this structure. This is why I needed to be a bit innovative; my class sizes are typically around thirty or more. Due to numbers I structured the seating in two circles (see diagram). A smaller circle, known as the Ring of Fire, and a larger circle around it, called the Outer Ring. In the center of both rings is one chair titled the Hot Seat. The implementation of the discussion occurs after some background work.