The best leader is one whose existence is barely known.
Next best is one who is loved and praised.
After that comes one who is feared.
Worst is a leader who is held in contempt and disobeyed.
If you cannot trust others, they will not be trustworthy.
The sage is quiet, and chooses his words carefully.
He completes his work, puts things in order, and lets the people say,
"we did this ourselves."
This verse appears to be made up of three sections, possibly of different authorship. The first and third sections explain the virtues of a Laoist leader: he is invisible, does not boast or claim credit for his achievements, and guides the people gently where they already want to go. It may seem strange that the authors consider a leader who is loved and praised to be worth less than one who is subtle, but this idea appears elsewhere in the Tao Te Ching, for example in a passage saying that the Way (implying natural action) is more valuable than love, compassion, or filial piety. The authors are primarily concerned with the leader not dominating the people, and instead leading them where it is natural for them to go. They would probably feel that a leader who is overly popular runs the risk of forcing some people to do unnatural things, as well as being tempted by his own power.
As for the line in the middle, we might ask how it relates to the rest of the verse. Unfortunately, as with other seeming non sequiters, I can only say that it is probably meant as a comment by a different author. It certainly expresses a truth about human nature: people appreciate being trusted, and placing your trust in someone is a great compliment that often inspires them to act in good faith. However, if you are always suspicious and accusatory of people, they might not feel any reason to be trustworthy. After all, if it doesn't make a difference in how you treat them, why should they care? I'm reminded of Gene Wolfe's opinion that if you do someone a great favor, it is actually you who are indebted to them, because you have had the honor of helping someone and they have suffered the embarrassment of needing your help.