A Galactica type battlestar is armed with at least twelve missile tubes. These are located behind the bow of the battlestar, at the fore of the vessel's midsection, with the tubes' launch doors opening on the dorsal side of the hull. As the outer doors open, the missiles are moved forward into launch position by powerful hydraulic rams.
Once the missiles are loaded into the tubes and are ready to be fired, they must be armed with a target package and a point of aim. This is typically ordered by the vessel's Commanding Officer, with the order being relayed by the Tactical Officer.
Conventional Warheads
It is likely that Colonial battlestars have the ability to launch missiles, either at ground targets or suitable spaceborne targets, armed with conventional, non-nuclear warheads.
While not strictly the same type of ordnance, other battlestars have been seen to fire ship-to-ship missiles (Hero). From this point, it seems likely that other, non-nuclear missiles exist for orbital bombardments as well.
Nuclear Ordnance
With Nuclear Groundstrike Missiles loaded in the tubes and ready to launch with the appropriate target information, the final stage before actual delivery requires for the Command Authority to specifically authorize the release of such weapons. Following such authorization, any officer aboard ship with sufficient rank to order weapons fire - the Executive Officer, for example - may order the release of the missiles.
Notes
While the release of biological and chemical weapons requires a presidential mandate (A Measure of Salvation), the release of nuclear ordnance, even used against planets and not just in space, does not seem to require the assent of the office of the President (The Eye of Jupiter).