Big thank you to /u/FutureWaves for linking my previous answer. I'd also like to add a little more, considering your question.
Saul Cornell, one of the leading academic figures into the study of the 2nd Amendment to the US Constitution actually discusses this at length in his book A Well-Regulated Militia: The Founding Fathers and the Origins of Gun Control in America. That said, he fortunately actually wrote an opinion piece for The Atlantic a couple of years ago that pulled some of his information into an easy to access format. I'm going to pull much of my information from either his book or his article "The Misguided Second Amendment Argument - Guns Have Always Been Regulated".
Regulation of a militia took shape in many different ways during America's earliest days. Contray to popular belief, firearm ownership was not super high prior to the American Revolution. However, once the war started things dramatically changed. Militia laws popped up in many states, which required men (usually between 16-60) to train with local militias. During the war, it was often once a month in many places, but it varied from state to state and even county to county.
One challenge that militias faced early on was that not everyone had firearms. Some were provided by militias, others borrowed them from shared facilities. Some folks actually showed up with fowling pieces, which are kind of like shot guns. These weapons are helpful to people living away from towns and cities, since it made hunting duck and small game easy, but it was useless on a battlefield. As Cornell points out, initial regulation said what men could or could not bring to militia musters. Here, Cornell said:
Without specific regulations and instead following common use or preference, most Americans would likely have shown up for active duty with fowling pieces, which were more like shot guns than muskets, because these were better suited for putting food on the table. In other words, the Founders recognized that if left to the free market and people’s own preferences, America’s militias would be prepared to hunt turkeys, not fight a powerful European standing army. A reliance on the market could have cost America its freedom. The various militia regulations enacted by states in the colonial period and after the adoption of the Second Amendment specified what weapons were required to meet the legal obligation of citizens to serve in the militia. Failing to report to the militia properly armed with the right weapon could result in fines.
Regulation also did take other forms as America tried to map out its own future during this period. An example of this could be seen during America's financial crisis of the the 1780s/1790s, where state legislatures actually said that during property foreclosures, militia weapons (and only militia weapons) could not be seized by creditors, that way that person could still serve. But here, militias still trained together with the idea that the government could call them up at a moment's notice to serve their purposes. It's important to realize that not every gathering of folks with guns were viewed, by the founders, as a militia. Shays' Rebellion is a prime example of the different.
Daniel Shays, a Revolutionary War veteran was angry at the corruption and unfair economic practices of the state of Massachusetts, so he gathered his own militia and they took up arms against the government. Benjamin Lincoln, another veteran, used his own money to call up his own militia and go against Shays. While these two groups looked nearly idenitical, the government and the founders viewed only one group as a 'militia' and the other as 'rebels.' In the eyes of the government, militias serve the government only.
Hope this answered your question. Please let me know if you have any followups.