Don't praise goodness, and people won't undermine each other.
Don't esteem wealth, and people won't steal.
Don't display treasures, and peoples' hearts won't become disturbed.
Therefore, the sage's way is to empty peoples' minds, and fill their bellies;
To weaken their ambitions, and strengthen their bones.
When people are without cunning, cunning men can't tempt them.
Practice non-action, and everything will naturally fall into place.
Does this verse sound too austere to you, with people being advised to give up all wealth and fame? Remember that the Tao Te Ching is written more in the style of proverbs than absolute laws. These proverbs, like our own, are meant to be applied to relevent situations, not prescriptively followed in all cases. For example, in English we have the proverb, "The early bird gets the worm," but we also have "Haste makes waste." These proverbs are not contradictory because neither is supposed to be applied to every situation. In a situation where quickness is needed, we say the first. In a situation where caution is better, we say the second.
The intention is probably the same with much of the Tao Te Ching's advice. A lot of it seems to be intended to stop people from doing something too much, such as esteeming wealth too much, or stimulating their senses too much. This is especially visible in the famous Verse 12, which states, "The five colors blind the eye; the five tones deafen the ear; the five tastes deaden the tongue." Were the authors of the TTC arguing that we should wear only gray clothes, eat only white rice, and wear earmuffs at all times? It seems much more likely they were arguing for not stimulating the senses excessively, and that is probably the best interpretation for Verse Three as well. Don't praise certain people too much, or there will be cutthroat competition. Don't worship wealth, and there will be fewer people willing to break the law to get it.
As for the lines about a full belly being better than ambition, this runs counter to American culture but is clearly what the authors of the Tao Te Ching had in mind: people being able to relax their ambitions and just take pleasure in natural things that are easy to get. In later chapters on politics, we'll see that the ideal Taoist government is not one that governs least, but one that the people can forget about because it's doing its job.