There are many coins in the US in circulation. They all have different designs. How was it decided what designs would be used for them?
The general design parameters originated with an Act of Congress:
In the Act of 1792, Congress mandated that all American coins show on one side "an impression emblematic of Liberty, with an inscription of the word Liberty, and the year of coinage; and upon the reverse of each of the gold and silver coins shall be the representation of an eagle, with this inscription, 'UNITED STATES OF AMERICA'. . . " Many changes in coin designs have been made since 1792; however, much from the original design scheme remains.
Beyond that the specific designs are created by the Mint after Congress passes a law (and the President signs, obviously), with the specific law dictating the general appearance.