The Republic consists of "thousands" of systems, represented by Senators. Power shifted to the executive branch - the Chancellor, elected by the Senate; the Jedi Council played an advisory role in the ruling of the Republic, and provided military support to the Republic's clone army, which answered directly to Chancellor Palpatine.
The Republic was at war with the Separatist Union, which was under the control of Chancellor Palpatine under his Sith alias Darth Sidious, via a council of leaders of the various subfactions composing the union.We also learn that, in the distant past, the Sith previously had been dominant in the galaxy.
The Separatist leaders were executed by the Chancellor's right hand man, Anakin Skywalker, aka Darth Vader. Upon the execution of the Jedi and the Separatist leaders, the Chancellor declared himself Emperor; the seeds of a resistance movement were founded by dissident senators and escaped Jedi.