My first step is to try and find something they know that I don't before crafting persuasive arguments. Maximize for total knowledge not winning arguments.
I'm kind of pissed that I guy I disagreed with seems to have been banned here, for example. I was curious where he was coming from and whether my foundation was as shaky as his appeared to me. (I think it was a guy, but I'll never know)
The best teachers I've ever had simply laid out all the evidence they deemed relevant and had us make up our own minds. The conclusion was never really in doubt by the teachers, but the process of arriving at it independently was more important than the destination.
I started out as a chemist (undergrad), became a statistician (grad), and finally realized that I had to design, run, analyze and fund my own experiments if I wanted something resembling "the truth", 9 times out of 10.
But my undergrad English teacher made me realize that it's more powerful to plant the seed of an idea and water it with evidence (selectively presented or not) than to try and outright convince people, when you have the luxury of time. I hope that my students are smarter for it; I let them sink or swim by their own wits and I expect them to ask for help if they find they're out of their depth. It's how the real world tends to work anyways.
EDIT: verb tense agreement