I've done the other three victories, now I'm going to try a diplomatic victory, but I'm not completely sure how to go about doing this. It seems like one way would be to focus on gold and just buy all the city-states votes. But that might not be enough, especially if some of them are conquered, so it seems like you'd also need to have a strong army to be able to liberate capitals and city-states for those votes. Am I on the right track or is there another way to go about doing this victory?
Also, OT, but is the only requirement for the military victory just to be the only civ still in control of its capital? Doesn't that mean it's possible to win this without doing anything if the AI civs conquer each others' capitals?
Your strategy is a good way of approaching this. When playing as Egypt I liberated several city states and had plenty of gold to ally with the rest. It can help to completely conquer some nations so as to reduce the number of adversarial votes. I have heard that liberating an ai civ will cause that civ to vote for you at the UN. You don't need to be ultra militaristic but it can help considerably to employ military solutions to assist with a diplomatic victory. However, city-states and their votes are the most important factors.
You just need to be the only civ in control of the original capital to win a domination victory. It does help if the ai civs fight each other since that reduces the quantity of capitals needed to prevail. You have to be kind of careful about certain civs amassing a high degree of power through conquest though.
Won my last game via diplomacy. Played as Egypt, took advantage of ganging up on England and took half the continent I was on. Basically I neutered all of the other nations on the same continent by taking over all the good resource areas. Then sold much of my army and gathered as much wealth as possible. On the other continent, the nations were constantly invading each other and by the time I built the United Nations, they were mostly broke. Vote time comes, bribed every other city state for easy 12 vote diplomacy win. Needed several thousand gold.
I won my first diplo victory after Russia had conquered the entire rest of the world with rifleman level units. I embarked on a massive liberation mission led by Chinese generals and mechanized infantry.
This is what I did, huge map, East vs West, NO city state, me and one other civ, tech till UN, build it. Vote needed to win will be 2 Whoever build the UN gets 2 votes I won without even meeting the other civ. Cheap? Yes, but it works!