Some notes on getting an earlier finish:
The difference between 1800ish and 1700ish finishes, at least for me, is primarily in the treatment of the midgame and endgame. Early games have a pretty obvious set of needed builds: granary, library, early academy at the start. University/Oxford, of course, National Epic, and Globe are also important (with the big food starts this is key). You also get the optimal civics (representation/pyramids, bureacracy/oracle, caste system, pacifism, usually with an OR interlude, environmentalism). Health buildings are nice, and the Great Library/Hanging Garden are useful if not essential.
Once you get past the opening, however, you have a long lull where there isn't a lot to produce. I accelerated my finishes by switching mines to windmills or abandoning them in favor of specialists. I also gained by pruning my tech choices, not going for anything that isn't on the critical path (e.g. no divine right, military tradition, democracy/comm/fasc). For cities with tons of food, slamming through chemistry/scientific method to medicine as quickly as possible also pays a nice yield. You can shave turns at the end by juggling commerce and production; once you get past electricity switching all eligible towns to watermills is a good idea. If you're heavier on hammers than beakers, go for computer before apollo; if not, go for apollo first.