To understand the term "well-regulated Militia" in context, one has to read the entire document and understand the history and usage. Militias prior to the Constitution were the primary defense of the States, and male citizens of a certain age were often required by law to own a firearm and register as part of the Militia for his state. Militias were not disbanded under the Constitution, in fact Article 1 Section 8 clearly enumerates Congressional power to create and oversee rules, training regimens and so forth to be carried out by the States in maintaining citizen militias for the purposes of, among other things, assisting in time of war, combatting insurrection, and other purposes. Many states no longer allow citizen militias beyond the National Guard, but many do. The Framers clearly intended for militia made up of armed citizens to be part of the national defense moving forward, and provided State and federal governments with the specific, enumerated power to regulate, train and appoint militia with that in mind. Moving on, the 2d Amendment states a "well-regulated militia being necessary to the security of a free state" as the context and rationale for the right of the People to bear arms. In this context, "well-regulated" obviously means well-trained, organized, prepared and functioning as a civilian defense force to be used for the national defense as well as for the domestic purposes set forth in Article 1 Section 8. The right to keep and bear arms belongs to the People and is a guarantee to the individual irrespective of formal militia membership... but its scope is limited to the context in which it appears and can be regulated accordingly.
The RIGHT to bear arms is not infringed by background checks.
The RIGHT to bear arms is not infringed by banning certain guns.
The RIGHT to bear arms is not infringed by documenting and registering guns.
See US v. Heller for a much more thorough explanation by much smarter people than I. ;)