Specifically, if you are going to discuss regression results, make a copy for the class. You are all very bright students, and getting together to discuss the article and your strategies for presenting it will make it a much better experience for everyone. Ask yourself which theoretical structure the paper best fits. Make clear up front what literature it builds on and how. Don't shy away from the regression results.
Social scientists love to communicate using statistics.
It makes us feel like we'll studying something real and concrete. Usually the regression results are key to understanding the main argument and findings of the paper. Don't sweat the equations too much. I'd start by reading the intro and the conclusion to the paper, and then read it through skipping over any equations. If the writer is good, she'll explain the equations in the text.