I play at the Emperor level and standard size maps at the standard speed with randomized leaders. Here are my general observations:
1. If you don't focus on rapid expansion early, you get crushed. Stonehenge and the Pyramids are nice, but forget it at the hard levels. There is no way you have the time and can risk the production. (If you are lucky, you can take the wonders in the soon-coming war.) The AI is all over you quick, and you need to prep for your first invasion. Wonders, exploration, fighting the barbs for city-state influence, etc. are all just luxuries you can't afford anymore. So forget Honor or Tradition, you gotta go for Liberty to get the expansion bonuses. In short, at the hard levels, my opening moves increasingly don't vary much. As a result, your first invasion goes like this: out of nowhere, some civ you've barely interacted with declares war and throws 10 units at you simultaneously. Because you have been building frantically and bought Liberty, you have almost no military and you lose two cities early. But then the AI's terrible battlefield choices (point 4 below) and your building of military units in all your cities turns the tide. At this point, your domestic production all but stops. You become the Soviet Union, building a massive war machine with little domestic infrastructure (libraries, granaries, etc). This allows you to nearly defeat the first invader, when suddenly another AI nearby attacks you also. Their city-state allies get in on the act (you don't have the cash to buy them, because you blew it buying emergency archers to survive the first wave earlier), as do the other AIs on the continent eventually. And pretty soon your fighting to take over the whole continent in a massive land war that occupies your from turn 50/75 to 300.
2. If you don't find research iron and settle around it, you're in real trouble. Increasingly I find myself bee-lining for iron out of necessity. Otherwise, I bee-line for crossbowmen as the only way to ward off swordsmen and long swordsmen I can't build.
3. You can't automate workers (or scouts) anymore. At the higher levels, the AI's quantitative advantages are so enormous, that you must take advantage of your superior human reasoning ability and micro-manage. I find this somewhat tiresome, as it slows down the pace, but it's the only way to prevent workers running all over the map, wasting three moves in pursuit of some tile far away.
4. Your only hope is to tactically outhinking the AI in combat. One recurrent problem in the Civ franchise is astonishingly bad AI military behavior. Units wander around in front of you cites to get hammered by your ranged units. AI units will embark for no particular reason, even though ranged units are brutally effective against embarked units. Wounded AI units don't retreat to get healed; they hang around the battle space for you to pick them off. The game makes up for this by giving the AI ridiculous quantitative advantages at the higher levels of difficilty. This is why about half-way through the game you get that astonshing pop-up that tells you that you have 400 gold, while the leading AI state has 50,000. The only possible way to overcome such insane stratetgic-quantitative advantages, is for the human player to tactically outfight the AI on the battlefield. This is why you must fight - its the only way to run down the AI's insane resource advantages. And this is also why the AI attacks you all the time at the hard levels: the difference engine of the AI reads a massive AI advantage over the human player and then it opts for war. Hence you get attacked so much, the game just turns into centuries of war (which is wildly unrealistic of course). The game would be far more enjoyable if the AI played better at the harder level and didn't just get more and more of everything in order to simply swamp the human player.
5. Diplomacy flies out the window except for resources swaps. Allegiance and cooperative play is all but impossible, because your AI 'allies' will turn on you on the drop of hat. This annoys me to no end, because it really shows how the AI is just a mathematical difference engine, and not a 'person.' Real world alliances don't just evaporate overnight like this; states don't march all the way across the world to fight someone they barely know. But the AI ignores the obvious geopolitical imperative of fighting neighbors and building sticky alliances. That way, it can attack you for no particular reason. Don't anthropomize the AI, which unfortunately turns the game into an exercise in game theory. Too bad MP doesn't work well too alleviate this, because at this point, I say no to just about every diplomatic solicitation, because I expect the AI to defect with no warning.
6. War of course is hugely expensive, so even after you take control of your continent and close in on the number 3 or 2 position, your happines and gold problems are so severe, that it becomes almost impossible to catch up. At this point, the leading AIs, who have dispatched their rvals with vastly greater ease than you ever could, build the UN or the spaceship and you lose. You try to build the huge fleet you need to invade the other island, but by that time your domestic unhappiness and bankruptcy have paralyzed you. Your techs and culture are way behind, because you were building units and war-buildings instead of domestic production (you're the USSR). You struggle to catch up, but there's no way you can buy the city-states you need to survive the UN vote (because you're broke and couldn't spend the culture buying the patronage tree). And you are loathe to switch you rationalism, because you had to buy piety just to control your spiraling unhappiness from all that imperialism. So sometime around turn 400-425, you lose. On the other hand, if you didn't fight all those wars, you never would have been big enough to take on the AI leaders anyway, so you're stuck.
At least, this is more or less how my games turn out. Thoughts would be appreciated.