President Eyring describes the process in this youtube video.
Henry B Eyring - Unanimity in LDS Church Councils
When I first came as the president of Rick's college I attended my first meeting that I'd ever been in, watching the General Authorities of the church, the First Presidency and others, running a meeting.
I had been studying for the ten years I was a professor at Stanford how you make decisions in meetings and groups. So I got a chance. Here's my chance to see the way the Lord's servants do it. Of which I now am one, but my first… I looked at it with my Harvard and Stanford eyes and I thought this is the strangest conversation I've ever…
I mean here are the prophets of God and they're disagreeing in an openness that I had never seen in business.
In business you're careful when you're with the bosses, you know. Here they were just…
And I watched this process of the disagreeing and I thought good heavens. You know I thought revelation would come to them all and they'd all see things the same way and some sort of you know…
And it was more open than anything I had ever seen in all the groups I'd ever studied in business. I was just dumbfounded. But then after a while the conversation cycled around and they began to agree.
I saw the most incredible thing. But here are these very strong very bright people all with different opinions. Suddenly the opinions began to just line up and I thought I've seen a miracle.
I've seen unity come out of this wonderful open kind of exchange that I'd never seen in all my studies of government or business or anywhere else.
And so I thought, oh, what a miracle.
And then it was President Harold B. Lee who was chairing the meeting. It was a it was a Board of Education meeting and I thought now he's going to announce the decision because I've seen this miracle.
And he said, “Wait a minute. I think we'll bring this matter up again some other time. I sense there is someone in the room who is not yet settled.” They went on to the next item and I thought, that is strange.
And then I watched somebody one of the Brethren one of the, I think one of the Twelve, walk past President Lee and say, “Thank you. There's something I didn't have a chance to say.”
So I want you to know the main thing you do about Harvard and Stanford, I love it, I hope this doesn't offend my wonderful friends. Forget it. We're in another kind of thing here. This is what it claims to be this is the true Church of Jesus Christ.
Revelation is real even in what you call the business kinds of settings. And a great man whom I love and will always love, President Harold B. Lee, taught me a great lesson that says, no, we can be open, we can be direct, we can talk about differences in a way that you can't anywhere else because we're all just looking for the truth.
We're not trying to win.
We're not trying to make our argument dominate.
We just want to find what's right.
And then a man sensitive enough to sense, without anybody saying anything, that somebody in the room was not settled. There's a kind of, there's a kind of process of openness and yet coming together and having confidence that you know what the Lord wants not what we want, that is, uh…
I loved Harvard I love Stanford had a great time their wife is here we spent the first ten years of our married life I was a professor at Stanford thought I'd stay there forever and had tenure and how happy we were and then went to Rexburg, Idaho, from there and then came down here and found out that there was a kind of making decisions and working together in groups that I have never seen anywhere else in the world except here.