One big point is to own our fallibility. Awareness of our limits and biases is a huge step in the right direction. Here are two other big, simple points I think are important:
- Actively seek out sources that you disagree with. We tend to surround ourselves with like-minded people and consume like-minded media. When we do check out our opponents, it tends to be the obviously fallacious straw men rather than sophisticated sources that could legitimately challenge our beliefs.
- Focus on the best points in the arguments against what you believe. Our opponents' good points are worth more attention than their obviously bad points. Yet we sometimes naturally focus on their mistakes rather than the reasons that hurt our case the most.