It has never been canonically established whether Romulan Senators are elected, appointed, or hereditary. However, we do know that Senator Pardek represented the "Krocton Segment" and was considered a "man of the people," so apparently public opinion can influence a Senator's power. We don't know if the "Krocton Segment" was a geographic location or some sort of ideological faction, or what.
We know from DS9's "Inter Arma Enim Silent Leges
" that the Senate determines membership in the Continuing Committee, and the Continuing Committee determines the Praetor.
The recent novel Typhon Pact: Rough Beasts of Empire
by David R. George III, however, establishes that the Romulan Senate is comprised of representatives of the one hundred wealthiest and most powerful Romulan clans -- making it fairly clear that the Romulan Senate is, in essence, a sort of House of Lords, comprised of the Romulan aristocracy. Each is appointed by the clan from which he or she comes, on the basis of the consensus of that clan's members and leaders.
Earlier novels, including Vulcan's Heart
, established that the Romulan Emperor remains the subject of an imperial cult, but that the Emperor is a mostly ceremonial position -- though particularly venerated Emperors sometimes compete with the sitting Praetor for power. Think of it as being akin to the way a British Monarch would sometimes compete with or exercise power alongside a Prime Minister back in the 1700s and 1800s. However, later stories, including the short story "Blood Sacrifice" from 2004's Tales of the Dominion War
, establish that the sitting Romulan Emperor was assassinated in 2374, shortly before the Romulan Star Empire entered the war against the Dominion, and that as of 2383 (Typhon Pact: Plagues of Night
), the Throne remains vacant.