What's the best way to present regression results in a conference?
I'd avoid presenting tables but would focus on (margin)plots that tell a story (which, of course, is based on your hypothesis/es). Here are a few links/references that might get you started:


Using Graphs Instead of Tables in Political Science
Interpreting and Visualizing Regression Models Using Stata
Graphische Darstellung regressionsanalytischer Ergebnisse (if you speak German) or Graphical Display of Regression Results