I was delighted to find this article, especially after recently blogging about people opting out of Thanksgiving this year due to political divides. If you are choosing to stay, these tools by the New York Times can help you argue your way through it - fairly.
1) Listen fully - not half-heartedly. Try to really understand what it is they have to say and not make it about proving that you are right.
2) Don't "Drop the Anchor" - meaning that a lot of people begin an argument without trying to understand how the other person came to feel or believe what they do, and "drop the anchor" without trying to move towards understanding.
3) Body language - refrain from the offensive ones, ex: eye rolling, patronizing hand gestures, stare downs, jaw clenching, or crossing arms & engage in the positive ones, ex: leaning forward and appropriate eye contact.
4. Don't Argue to Win - because you won't, convincing someone of your opinion is not likely to happen in one incident or over a single meal. Arguing for the sake of testing and improving one's opinions and gaining understanding of the other's viewpoint is ideal.
5. Know the Facts - All of them.
6. Speak & Listen Fearlessly - Don't be afraid to voice your beliefs and don't be afraid to listen to ones that oppose yours. It can be difficult, even offensive and scary, but through that courageous act is the only hope to find common ground.
You can find a link to the full article here.