The primary objective of the Sith was to achieve full mastery of the dark side. Mastering the dark side provides the Sith with power, and power allows them to rule over the galaxy. Ruling the galaxy may not be an explicit, separate goal of the Sith, but it is inextricably linked to their objective of mastering the dark side. In other words, the Sith could not truly say that they had mastered the dark side if they weren't also able to use it to rule the galaxy. This is stated most explicitly as follows:
But it was here that they would one day work together the way Sidious and Plagueis had to coax from the dark side its final secrets. In the intervening years he had actually come to appreciate Plagueis for the planner and prophet he had been. Such perilous machinations required two Sith, one to serve as bait for the dark side, the other to be the vessel. Success would grant them the power to harness the full powers of the dark side, and allow them to rule for ten thousand years.
Tarkin, p. 101
The Sith believed that the act of harnessing the full powers of the dark side would allow them to rule the galaxy for ten thousand years. Accomplishing their primary objective would imply that the Sith also ruled the galaxy, even though ruling the galaxy was not necessarily an explicit objective by itself.
The link between ruling the galaxy and the Sith ultimate goal of mastering the dark side is also stated as follows:
...he would not allow himself to be sidetracked from his goal of unlocking the secrets many of the Sith Masters before him had sought: the means to harness the powers of the dark side to reshape reality itself; in effect, to fashion a universe of his own creation. Not mere immortality of the sort Plagueis had lusted after, but influence of the ultimate sort. As his Empire swelled, bringing more and more of the outer systems into its fold, so too would his power unfurl, until every being in the galaxy was held captive in his dark embrace.
Tarkin, p. 242
Sidious believed the dark side would give him such power that he would be able to fashion the universe however he wanted. Since Sidious craved power, he would of course fashion the universe such that he ruled the galaxy (and the rest of the universe).
As an analogy, suppose you are a businessman whose goal is to acquire a monopoly in a certain industry. You may not have an explicit goal to acquire control over the smallest company within that business, but accomplishing your monopoly goal necessarily implies that you control the smallest company. You don't have a monopoly, by definition, if you don't control all companies in that industry -- even the smallest.
Legends is more explicit that ruling the galaxy by taking over the Republic was a goal of the Sith plot which had existed since Darth Bane's time (called the Grand Plan):
The goals of the Grand Plan were revenge and the reacquisition of galactic power. But while most Sith Lords since Bane had in their own fashion helped to weaken the Republic, their efforts had owed less to selflessness and allegiance to the Rule than to weakness and incompetence.
[Palpatine] was a manifestation of dark purpose, helping to advance the Sith Grand Plan and gradually gaining power over himself so that he might one day—in the words of his Master—be able to gain control over another, then a group of others, then an order, a world, a species, the Republic itself.
Darth Plagueis, pp. 78, 171