How can an issue be put on a voting ballot in America?

It varies from state to state. But generally speaking there are two ways.

The first is for the appropriate governing body -- city council, county commission, state legislature -- to put an issue on the ballot. Almost every state allows this option and-- as many states require voter approval for bonds and taxes -- this tends to be the most common.

The other way -- which is only allowed in some states -- is via a citizen-initiated petition. In those states that allow citizen petitions, there are different rules as to how many signatures are required, whether there is a distribution requirement (e.g. a certain number in each congressional district or a certain fraction of congressional districts), and whether the rules differ based on the type of proposals -- statutes/ordinances vs. constitutional amendments/charter amendments.