How did the Death Star move?

In the Star Wars saga, one of the most iconic weapons of the Empire was the Death Star: a self sustained weapons platform the size of a moon, with the capacity to destroy a planet. in A New Hope, we see the first Death Star in close proximity to the planet Alderaan, holding the planet hostage as the Empire tries to deduce the location of the Rebel Alliance's headquarters. In Return of the Jedi, we see the second Death Star in "dry dock" over the forest moon of Endor as it is being constructed.