How did American leaders convince ordinary people to join the militias to fight in the Revolutionary War?

The arguments were different based on where the militia was located. In the South, after Banastre Tarleton executed Americans, and the British army promised freedom to any slave who assisted their cause, fighting for the colonial militias was a way to preserve the social order of slavery or a way to avenge those deaths caused by the British killing prisoners of war.  
Throughout the colonies, the patriots fought in order to remove the invading British armies. They fought to defend their homes. Few soldiers were so touched by the tax issues of the day to make it their main motivation for fighting; however, many had to face some kind of British rule that they disliked.
The British also used German Hessians—these mercenaries were considered the most vicious in all of Europe. Many patriots fought because they thought that the British were treating the American colonies as occupied territory rather than land occupied by British subjects. Many preachers even called it "God's work" to defend the natural rights of the colonists by fighting against British rule.