How did tyrants attempt to gain the approval of common citizens?

The tyrants in Ancient Greece used different methods as to how to gain the approval and support of the ordinary people, but eventually it was basically led to prosperity and peace.

The tyrants were proclaiming themselves as wise people, people who have knowledge of lot of stuff, have military experience, and that they are people with strong character.

They were also convincing the people that they will bring in peace and wealth to the city-state by the using of politics and trade.

In the people of that time, that was more than enough, though they always were keeping an eye of what was happening.

Also, you should note that in Ancient Greece, the word tyrant was not used as nowadays and that it is necessarily a bad term, but it was used for a person that had big power in the society and controlled it, in a similar way as a monarch.