Read the stories on DU and elsewhere where DU'ers turned right wingers around. It usually happens when the good guy is able to manoeuver them into a position where they have to admit that to believe cherished point A they have to believe point B which goes against their beliefs. That's cognitive dissonance and starts their own internal dialogue which will erode the foundations and crumble their facade that is willfully ignorant of reality.
You have to begin by being friendly. That's why all the screaming and rabid foaming at the mouth that goes on here (and on the other side) is counter-productive and unhelpful to say the least.
The Scaffolding of Rhetoric, by Winston Churchill:
http://www-adm.pdx.edu/user/frinq/pluralst/churspek.htm
How to be as persuasive as Lincoln:
http://thinkprogress.org/climate/2009/02/16/203702/abraham-lincoln-figures-of-speech-shakespeare/?mobile=nc
Abraham Lincoln, Master Persuader:
http://www.prmuseum.com/burger/chet_lincoln.html
"If you would win a man to your cause, first convince him that you are his sincere friend. Therein is a drop of honey that catches his heart which, say what he will, is the great highroad to his reason, and which, when once gained, you will find but little trouble in convincing his judgment of the justice of your cause, if indeed that cause really be a just one.
"On the contrary, assume to dictate to his judgement, or to command his action, or to mark him as one to be shunned and despised, and he will retreat within himself, close all the avenues to his head and his heart; and though your cause be naked truth itself, transformed to the heaviest lance, harder than steel, and sharper than steel can be made; and though you throw it with more than Herculean force and precision, you shall no more be able to pierce him than to penetrate the shell of a tortoise with a rye straw.
"Such is man, and so must he be understood by those who would lead him, even to his best interest." -- Abraham Lincoln