As far as I am aware, we don't have any documents explicitly explaining the strategy for introducing specifically minted coins of specific, standardized valuations.

However, we can track the development of these coins, and form some hypotheses.

Prior to standardized coinage, economic exchanges used weighed measures of silver, in broken pieces called hacksilber. As King and Stager write in "Life in Biblical Israel":

weighed metal (usually silver) was used as "money" for transactions in the Ancient Near East (p. 174)

The silver hoards that we have found archaeologically are basically full of pieces of silver, pieces of jewelry, and cut pieces, all small. These would have been placed one by one into a scale pan, and weighed with a stone or lead weight of standard measure (usually measured in "shekels"), much like this. If the silver pieces were too big or heavy, they would be cut to size, so that the appropriate amount of silver would exchange hands.

Eventually, people decided that they could cut out all that annoying cutting and weighing by making their metal into standardized pieces marked with their weight. They were already doing this with ingots of raw materials (such as copper/bronze, glass, iron, etc), so the concept wasn't that much of a stretch. The practice appears to have originated among merchants, as they used small silver blobs or "dumps" as a sort of pre-coin, but had to be stamped in order to help with acceptance as a mark of standardization. It was these metal quasi-coins that began to gain prominence, gradually and through use over time, until the rulers of the Anatolian kingdom of Lydia developed official examples of standardized weights of precious metals for use in economic exchanges, minted and marked with official markings to approve their value (Glyn Davis, History of Money p. 62). We don't have records of how exactly they were introduced into circulation. However, one may assume that it was gradually as the government bought supplies from merchants with the coins, and those merchants bought other things as well, and the coins propagated through Lydian society, and through Lydian trade partners.

Coinage was a logical next step after the practice of weighing a certain amount of metal out for an exchange. It was much easier to simply possess small pieces of metal which were already weighed and marked by the government to ensure their accuracy and trustworthiness.

Other ways of purchasing remained alongside the coins for a long time. Other groups did not begin using coins for hundreds of years. The Romans, for example, did not start using coinage until approximately 300 years after the Lydians, and therefore international merchants would have had to be able to deal with not only the coinage currency, but also hacksilver.

I would especially like to hear about how Carthage did it if any one knows.