It would start with a commitment to the idea, to recognize that forcing policies, on everyone, that half the country hates, is stupid. The idea behind consensus isn't that everyone agrees. And it isn't majority rule. It means that no one has paramount objections to the policy proposed. The root word of consensus is consent, and it means everyone consents to the decision, even if they don't necessarily agree with it.
But if a significant portion of the citizenry does have a paramount objection, a simple majority isn't good enough. We can't do that policy. The idea is to avoid passing laws that leave one side angry, resentful and spoiling for revenge.
The mechanics of consensus vary, there are many different systems, but they all focus on the above as the goal. A simplistic move in that direction would be to require a two-thirds majority vote on all national legislation. People will insist that Congress would completely stall, unable to do anything. I don't believe that. Faced with the two-thirds requirement, they would find enough common ground to get the necessary work of government done. They might not come together on one side's favorite social engineering scheme, but that's sort of the point. Moreover, this requirement would give a real leg up to candidates who were able to "play well with others". The tone and tenor of Congress would change.