Via cultural domination in the early 1970's 
It was a LOT of fun, and I learned tons. Being an old Colonization (the game everyone thought sucked) nut, a lot of the game was similar - only bigger and better. So it was pretty cool. I did run into a lot of things though...
Funnest thing: All the cities I managed to flip over to my side! I got like 3 English, and 2 Iroquois, so I was pretty happy.
Most frustrating thing: One English city in the middle of my territory and completely surrounded with my own cities desperately cranking out culture-buildings. It would not flip! I did push it back into a 9 tile square, but I guess it was too well developed (8 pop?) to flip for me. And by the time I was able to spy on them (for propaganda), they had gone to democracy! Stupid English!
Dumbest thing: The AI's attempt at "trades". Sanitation for a world map? PUH-LEEZE! I guess I really need some tips in this department, because nomatter what I tried, the AI just did not want to trade ANYTHING (besides for my maps). I had a global monopoly on spices, but do you think I could get anything for them? No! How stupid is that?
Most suprising thing: The AI's being huge chickens. Two large continents with 3 AI's each (and me huddled away on my private island) - you think they'd fight, right? Nope! Not one fight. No tussles, scraps, or even stepping a foot over enemy territory (except mine, of course)! They just sat there, doing nothing. I had to personally start the world's first war, hoping it would set off some fireworks. So I aimed for the Celts (who had 5 cities, but lost one when it flipped to Russia) because they were the weakest and most pathetic culture. Poor buggers were still stuck in the stone age while the rest of us were rolling out the infantry. So I lined up a whole bunch of Guerillas outside their borders and went knocking:
"Give me this city."
"Sorry, I don't think thats possible."
"Give me this city, NOW."
"Sorry, I don't think thats possible."
"GIVE. ME. THIS. CITY."
"Sorry, I don't think tha.."
"Oh #(*$ you."
So I charged in with my troops and captured three cities in two turns. I was wading through their knights (hehe) that were defending the road to their capital when suddenly Russia declares war on the Celts too, and marched right in from behind with Cossaks! HAHA!
So yeah, that was the end of them. Unfortunatly I kind of forgot that I had a RoP agreement with the Celts at the time, so after that all the other nations wouldn't exchange RoP with me. I was like "Oops" for a bit, and then I realized I was almost done my tech rush to aircraft. Who needs RoP when you're the only one that can fly?
Most annoying thing: Pollution. Ugh. My main island was pretty much a cesspool by the end of the game. I had like a dozen workers just jumping from mess to mess, constantly. Fortunatly I had layed RR tracks on every square inch of the island, so getting around wasn't a problem
All in all though, it was great fun, and a huge learning experience! I'm just about to fire up another game and see what happens - hopefully there'll be more fighting this time!
Cheers
(PS: Any tips on trading with the ******** AI would be welcome!)

It was a LOT of fun, and I learned tons. Being an old Colonization (the game everyone thought sucked) nut, a lot of the game was similar - only bigger and better. So it was pretty cool. I did run into a lot of things though...
Funnest thing: All the cities I managed to flip over to my side! I got like 3 English, and 2 Iroquois, so I was pretty happy.
Most frustrating thing: One English city in the middle of my territory and completely surrounded with my own cities desperately cranking out culture-buildings. It would not flip! I did push it back into a 9 tile square, but I guess it was too well developed (8 pop?) to flip for me. And by the time I was able to spy on them (for propaganda), they had gone to democracy! Stupid English!

Dumbest thing: The AI's attempt at "trades". Sanitation for a world map? PUH-LEEZE! I guess I really need some tips in this department, because nomatter what I tried, the AI just did not want to trade ANYTHING (besides for my maps). I had a global monopoly on spices, but do you think I could get anything for them? No! How stupid is that?
Most suprising thing: The AI's being huge chickens. Two large continents with 3 AI's each (and me huddled away on my private island) - you think they'd fight, right? Nope! Not one fight. No tussles, scraps, or even stepping a foot over enemy territory (except mine, of course)! They just sat there, doing nothing. I had to personally start the world's first war, hoping it would set off some fireworks. So I aimed for the Celts (who had 5 cities, but lost one when it flipped to Russia) because they were the weakest and most pathetic culture. Poor buggers were still stuck in the stone age while the rest of us were rolling out the infantry. So I lined up a whole bunch of Guerillas outside their borders and went knocking:
"Give me this city."
"Sorry, I don't think thats possible."
"Give me this city, NOW."
"Sorry, I don't think thats possible."
"GIVE. ME. THIS. CITY."
"Sorry, I don't think tha.."
"Oh #(*$ you."
So I charged in with my troops and captured three cities in two turns. I was wading through their knights (hehe) that were defending the road to their capital when suddenly Russia declares war on the Celts too, and marched right in from behind with Cossaks! HAHA!
So yeah, that was the end of them. Unfortunatly I kind of forgot that I had a RoP agreement with the Celts at the time, so after that all the other nations wouldn't exchange RoP with me. I was like "Oops" for a bit, and then I realized I was almost done my tech rush to aircraft. Who needs RoP when you're the only one that can fly?

Most annoying thing: Pollution. Ugh. My main island was pretty much a cesspool by the end of the game. I had like a dozen workers just jumping from mess to mess, constantly. Fortunatly I had layed RR tracks on every square inch of the island, so getting around wasn't a problem

All in all though, it was great fun, and a huge learning experience! I'm just about to fire up another game and see what happens - hopefully there'll be more fighting this time!
Cheers
(PS: Any tips on trading with the ******** AI would be welcome!)