How to use "correctly" in a sentence

If I read the temper of our people correctly, we now realize, as we have never realized before, our interdependence on each other; that we cannot merely take, but we must give as well; that if we are to go forward, we must move as a trained and loyal army willing to sacrifice for the good of a common discipline, because without such discipline no progress can be made, no leadership becomes effective.

'But the point is, that each thing has got to be explained correctly

On the third day, if I remember correctly, I saw a boy killed

We thought they were some sort of Red Indian food, and, to cook them correctly, it was necessary to do special dances with magic words.