I've never even come close to the domination victory, because there is so much land. Don't you need like 40% or something? All the land settled by the "major" civilizations doesn't amount to that much, and settlers are insanely costly in the scenario to go settle iberia, gaul, and germany.
I've "won" a conquest victory with the Romans, and later on with the Persians. I say "won", because I beat all of the civs, it said there are 0 opponents left, but I didn't win. At that point I figured that to "win" I had to beat all of the "minor" civs too, and I didn't have enough time left to go crush the Germans. Sadly, a couple months later, I did the same thing with the Persians. In that game, I probably had time to go take out the germans and whatever the gold coloured civ in the crimea is, but didn't bother because I'd been building shrines instead of military units for about 20 turns to save time.
Easiest conquest is probably with Persia:
Early Strategy:
1) send two immortals and an archer straight north to take that city.
2) send an archer and a settler SW to found a city on the coast with access to flood plains. Later on irrigate them; this is a worker factory for me.
3) build Persian capital where it is. build a granary and a barracks and then start pumping out immortals. When you hook up to the Copper nearby, start pumping out axemen.
4) send all your other immortals into India, and take out the city between you and India, then both indian cities. AFter India, go north of the mountains, and start taking out the barbarian cities there. The one directly north of india looks like crap, but mine 2 grassland mountains, build a barracks, and it will pump out a vetran immortal every 3 turns for the entire game.
I usually wait until I've taken all the barbarian cities in the north before attacking babylon. You want to make sure you have a pretty good mixed army. I usually build:
Elephants in the northern indian city.
Archers in the southern indian city and the city south of that.
Axemen in the capital.
Horse archers in one of the two cities in the plains to the north, immortals in the other.
Swordsmen in the city two north of the capital, though this probably should be axemen -- I just like to build some of every unit, and you almost have to build all the others.
Spearmen in one city somewhere.
The most southern babylonian city pumping out workers.
Babylon pumping out workers unless they get a great engineer; then build the shrine with him and pump out missionaries.
Build Immortals *everywhere* else. Never attack anybody with anything but an immortal unless you have > 90% odds or you are attacking a spearman.
Get every immortal both flanking promotions. Then they retreat 60% of the time. This means that even if you attack at 0% odds to win, they have a 60% chance of surviving. You'll absolutely own anything that isn't a spearman. These guys can take down Prats (it takes a few, but only 40% of them die).
Take out arabia reasonably early, or you'll end up with arabia full of spearmen, which are nasty, because your main force will be immortals.
In terms of Arabia, and Egypt when you get there, and even north of Macedon/Greece: get the visibility promotion on some of your immortals and get rid of the fog of war. The barbarians in Africa are absolutely nasty.
Also, beware that at about 1AD barbarians stacks will start showing up randomly in places that you didn't think they could, so make sure you have a couple archers in every city.
Once you've got enough of the immortals running around, you just need to wait for the axemen to catch up when you run into spears. Note that you can take down a str 5 spearman in a city on a hill with about 7-8 immortals; bring 10 to help the 4 or 5 which retreated heal. You lose a *lot* of immortals (I think I lost well over 50 of them over the course of the game), but most of your crap cities will be building one every 3,4, or 5 turns. Better cities build more expensive units, or archers for defense.