What do the terms arms, well regulated, and militia mean in the Second Amendment?

I swear we've collectively answered this before.At the time the 2nd amendment was written, the term "well-regulated" meant, essentially, "in good working condition."  This meant "working weaponry with sufficient munitions to fight with them."Also at the time, the USA had a very limited standing national army: the overwhelming majority of its military strength came from citizen militias, with each member of the militia providing their own weapon, not their state providing a weapon.TL:DR:  The militia relied on each member, a private citizen, to provide their own personally owned weapon and some ammunition.

Lots of answers have answered this question well, so I won’t duplicate efforts. Let me just concentrate on “well regulated.” What many who hate guns misunderstand is that this term “well regulated” does NOT refer to owning firearms, but to the a well organized, well led, well-disciplined, and sufficiently supplied militia—or body of civilian armed men.There were NO other laws at the time regulating firearm ownership or the bearing of firearms, so it doesn’t make sense that they intended owning and bearing firearms to be regulated by the federal government.I’m sure the founders of this country would be shocked to see how misunderstood their wording has become in modern days.

The "well-regulated" clause really refers to training.  There were "regular" militia, who were trained to fight as blocks of soldiers, and there were "irregular" militias who just ran out with their guns.  From that perspective, the situation is not unconstitutional.  Unwise, but not unconstitutional.

We have a God given right to defense. We are the people. That is the individuals with no organization required. The militia is all the people. The level of organization is similar to a neighborhood watch or less and is optional. Well regulated means to meet once or twice per year with a neighbor or a friend or two. Level of training is maybe 7 days training per life though more is better. Keep arms means you can buy, build, fix and store. Bear arms means you can carry arms at home, work, in the community and on travel. Free state means the condition you live in and the State you live in, similar to the original Colonies. It does not mean the federal government. Shall not be infringed means the Federal, State and Local government cannot mess with this God given right.

The syntax seems to suggest to me that the formation of a militia is more of an option than a demand. The Constitution protects their right, not their duty, to form and maintain a militia.

"A well regulated diet being necessary for the health of a free state, the right of the people to eat and grow vegetables shall not be infringed." What is protected in that sentence, diet or food?

The inclusion of clauses in documents such as here are usually informative and intended to provide some partial context for other provisions that are more substantive. To a reader in the 21st Century a document written in the later 18th Century often is to decipher or fully understand because of the absence of requisite historical context. And possession of the historical context is essential in many cases, particularly with respect to the Second Amendment to the U.S. Constitution. Now some would hold that the reference to "militia" is outmoded and the necessity of a "militia" made obsolete with the creation of a standing army. But that would seem to betray the lack of historical awareness by that person as it ignores the great aversion that was held by the Founders in 1787 when the Constitution was drafted. Indeed most people are only aware of the myths of the Revolutionary War and the notion that Washington won an 8 year war with only militia troops. Far from it. Recall that the Continental Army was created and Washington named commander a year prior to the Declaration of Independence. General Washington and a number of officers had significant military experience as adjuncts to the British Army in the French and Indian War in the 1750's and knew well that militia could not be successful against a professional force, even though the Continental Congress thought that the militias were sufficient. This delusion was made credible by the significant cost to the British in the Bunker Hill action, but that was a static defensive action fought from improved positions and not a field army facing a field army. The battle of Long Island and NYC proved Washington correct. Rather the notion of a militia being a reference in the 2nd Amendment was a hat tip to the more fundamental value of having an armed populace that was able to contest actions and defend their rights from encroachment. While in their day they would be organized by community and drill together, this was not a necessity. Consider the 4-6,000 that converged on the days of and after Concord,  a number that swelled to over 12,000 around Boston and lead to the Boston Siege and the Bunker Hill battle. They did not train together until they arrived. It was necessary that they all be armed and well acquainted with the use of their own weapons in order to join together to rebuff the force of arms arrayed to subjugate them.  Without widespread individual gun ownership as a matter of right you could never constitute a "militia" and could never resist tyranny. That's why the reference to militia is there: because in 1787 they already saw the need for the capability of individual defense even if a standing army was available.

Well, there isn't really a need for a "well-regulated" militia anymore. Even though people still like keeping their guns and thus use that sentence frequently as an argument for their Second Amendment privileges, they probably don't want to waste their time organizing into a militia. If they did, then they would join the National Guard or something like that.

Because states need to be able to quickly raise well-trained bodies of men  to fight, all citizens (which at the time meant white males) must be allowed to own and use arms. That is the obvious grammatical meaning of the amendment.  You didn't ask for background or justification, but I will add two ... points of personal preference.  I do not think the current court ruled "correctly" when they said the amendment protects an unqualified individual right to keep and bear arms and sincerely hope some future court will overrule that.  However, until that happens it is also now a part of the law of the land  I also do not see how anyone could think that amendment with that first clause clearly ruling the second, could be about personal self-defense.  It seems so obvious to me to be about State defense at a time when most everyone was fearful of standing armies.