The Second Amendment "grants" nothing. The right to keep and bear arms is not a right granted by the Second Amendment, nor is it in any way dependent upon it for it's existance.
A right is a natural thing that individuals possess. The right to keep and bear arms exists outside of any government entity. A state is a government entity. The states had the "power" to arm their militias which were comprised of a subset of "the people" at the time. The Second Amendment stopped the "Central Government" from disarming the people, and one reason for this was to make sure that the states had well regulated militias, which could not be disarmed since the people could not be disarmed. If the state militias were comprised of a subset of the people, and all of the people had their rights to keep and bear arms secured by the Second Amendment, then the subset of people comprising the state militias also had their rights to be armed protected. By logic then, the state militias could not be disarmed by the "Central Government".
The Second Amendment prevents disarmament of the state militias through the protection of the people's right to keep and bear arms. The two clauses are connected, but the operative clause is not dependent upon the prefatory clause as some of the anti gun folks have tried to argue. The Heller case should put that arguement on the trash pile as we go forward with the debate. Nordyke also makes a point that the Second Amendment holds against the states as well. Thus, the states cannot disarm their citizens if this holds and gets a hearing at the USSC, eventually.
"If you love wealth better than liberty, the tranquility of servitude better than the animating contest of freedom, go home from us in peace. We ask not your counsels or arms. Crouch down and lick the hands which feed you. May your chains set lightly upon you and may posterity forget that ye were our countrymen." Samuel Adams.