Can you translate it?
The right to own a firearm is an individual right and is unconnected with service in a militia. The 2nd Amendment opening clause that refers to a "well-regulated militia" should not be interpreted as limiting or expanding the individual right to keep and bear arms.
The Court briefly addresses the historical reasons for the Amendment and finds that the idea was to to deny Congress the power to "abridge the ancient right of individuals to keep and bear arms" so that the Federal Government would not be able to disarm the people in order to disable the citizens’ militia.
The Court did find that none of the precedents conflict with their current interpretation. They also addressed the issue of limitations on the 2nd Amendment:
"Like most rights, the Second Amendment right is not unlimited. It is not a right to keep and carry any weapon whatsoever in any manner whatsoever and for whatever purpose: For example, concealed weapons prohibitions have been upheld under the Amendment or state analogues. The Court’s opinion should not be taken to cast doubt on longstanding prohibitions on the possession of firearms by felons and the mentally ill, or laws forbidding the carrying of firearms in sensitive places such as schools and government buildings, or laws imposing conditions and qualifications on the commercial sale of arms. Miller’s holding that the sorts of weapons protected are those “in common use at the time” finds support in the historical tradition of prohibiting the carrying of dangerous and unusual weapons."
Reasonable restrictions only, in other words. D.C.'s handgun ban was not reasonable:
"The District’s total ban on handgun possession in the home amounts to a prohibition on an entire class of arms that Americans overwhelmingly choose for the lawful purpose of self-defense."