One primary way that the community in Lois Lowry's novel, The Giver, is kept under such strict control is the demanding and unending sets of rules to which all citizens must adhere. There is no allowance for independent thought or action, and every minute of the day is specifically laid out for each person. The few citizens who fail to comply are "released," as are the more aged members in order to keep food supplies sufficient. Citizens believe everything that is told to them, and they rely totally on the rulers who organize their lives.
This is a very good question and one that I am not really sure that we know.
We do know one way the community keeps things under control. That is through "releasing" people who are too much trouble. That would be a very good way of keeping things controlled because anyone who makes trouble ends up dead.
Another possible thing that is going on is that they have no families and things like that. So if someone is released, there is really not anyone to miss them.
Finally, I would say that they keep things organized by forcing the Sameness on everyone (though I don't know how they make the weather be the same all the time). By making everyone be the same, they take away a major source of conflict.
In making an inference based on what I read in the book about the community one of the first things that the community elders did was to set up things so that there is no deviation from a serious set of social, physical, and environmental norms. They set-up a climate controlled system in a region that is protected by security that prevents planes from flying overhead and responds if they do come.
They restricted the number of children a couple could have and set-up a system fro births and death. Then, when they had everything in place the way that they wanted it to be they somehow gave all their memories to one person to carry so that they could function in a machine like state with no deviations except for different talents and skills that only surface to a mediocre degree.
Their is no real definition in the book as to how the changes came about or how things are kept under control other than by close monitoring of the people and the standards of sameness.