I usually play one of two types of game: Earliest landing on AC, or personal highest score at 1500AD (after that it gets a bit boring).
Playing Deity + 7 Civs, I usually get well in front of the pack by 1AD in both tech advances & number of cities. From there on it's just a matter of controlling the other civs while pushing forward for a winning score.
My strategy is:
* rapid early expansion & exploration using Horsemen, Chariots or Diplomats
* kill off any small & weak civs on the same continent, make contact with civs on other continents
* aim for Monarchy ASAP, avoid collecting other techs that do not lead to Monarchy
* build Hanging Gardens to keep the plebs happy in far-flung cities
* build Pyramids for quicker population growth (I might revise this in light of info gained from other forums), use Caravans to build Wonders & expand population in the larger cities
* continue to build new cities until they start to become unmanageable, then use Settlers to add roads, mines, irrigation, etc
* aim for Democracy ASAP, making sure to get Leonardo's Workshop along the way (usually I have Democracy by 500BC)
* avoid getting Feudalism so that the cities can continue to build Warriors & not forced to go to Pikemen
* build Statue of Liberty and switch to Fundamentalism - this allows building lots of units in all cities & also accumulate gold reserves if needed - use Settlers to build lots & lots of cities
* use Diplomats to convert foreign cities rather than attack with troops - defend my cities by bribing foreign troops
* by 1AD I will typically have 80-100 cities & have other civs reduced to a handful of cities each
* avoid getting Gunpowder until after Railroad - gives plenty of time to accumulate lots of Warriors
* build Darwin's Voyage & collect Gunpowder & Explosives with the +2 techs - keep building Warriors in around half of the cities & disband the upgraded Musketeers in some of the other half to quickly build city improvements
* aim for Conscription so that the Warriors (cost 10 shields) will ultimately become Riflemen (disband value 20 shields)
* use Engineers to connect all cities with railroads
* at some point, new cities can build units without having to support them (ie. support = "NON") - at this stage build a scattering of cities & move units to these to become unsupported
* switch to Democracy, crank up Science, & go for broke on tech advances
* build lots of Freight, move them to the NON-support cities & then to other cities to increase population
By this stage, there is little interaction with other civs as they are reduced to a few cities struggling to survive (I try not to wipe them out altogether, unless they are getting in the way). Each turn can take quite a while (15-20 minutes) because of the number of units being built & moved, so unless I am aiming for a personal best score I might abandon the game at this stage. Otherwise, press on with increasing population, tech advances & building Wonders.