The question is really in the title. How did the terms “right” and “left” become synonymous with “conservative” and “liberal” respectively? It is my understanding that in some European countries, the terms have the opposite meanings (ie, the Left is the conservative movement). Any information would be greatly appreciated.
I’m equally curious on this issue. I have observed that the way seating is arranged in the houses of Congress (USA) there’s definitely a Right and Left dichotomy, although it appears to be a party issue more than a political leaning issue, if you can accept that there are Right and Left Democrats as well as Right and Left Republicans.
There doesn’t appear to be a way for the Center-leaning people to have distinctive seating. And the Radicals are usually on camera out in the lobby. 
It’s from post-revolutionary French Assembly seating positions. (see here)
As for the “left = conservative” thing, I don’t think so. However, the term “liberal” can mean various things - the main conservative party in Australia is the Liberal Party, for example.
I’ve heard that in Russia, the left was considered the “conservatives” because in the days of the Soviet Union, the left was for the status quo(communism) while the right was for change. However, take this with a large grain of salt, because I’m pretty sure that I picked that tidbit up from a Tom Clancy novel.
It’s my understanding that the French associated conservatives with “the right” and liberals with “the left” even before the revolution. Typically the King’s chief minister was referred to as his “right-hand man”, and did, in fact, sit to the King’s rightat meetings and public appearances. Obviously this person was expected to be a fierce royalist and opponent of reform in most cases. (This information comes from Jack Fincher’s Sinister People: A History of the Left-Handed.)
Sum of All Fears. Yeah, that’s what sparked the question, actually. Heh.
Yes, and in some European countries, a “liberal” is typically someone who favours a greater reliance on the free market, which isn’t quite what “liberal” in the North American sense refers to. So we could say that in some countries, “right = liberal” (or rather, some right-wing ideas are called liberal).