Control the World Congress, control the end game
The World Congress becomes possibly the deciding factor for the rest of the game from the moment it's founded. Other than enabling Diplomatic Victory, it allows you to cripple your rivals by non hostile means... though they can do the same to you. It can give you a leg up on other victory types with shared wonders and mandated research funding. Ignore it at your peril.
By extension, City-State allies are now even more important, as they come to represent a majority of the possible votes in the World Congress as the eras draw on. I haven't played a single game of Brave New World in which I didn't end up taking the Patronage policy tree to exploit this. Be nice to the little guys, and their votes will lead you to dominance.
How I learned to stop worrying and love the new ideology system
Ideologies (Freedom, Order, and Autocracy) have changed a fair bit. You now have an incentive not to join the prevailing world ideology, as the first civ to choose each branch gets two, free policies. They also now tie into the tourism system. Civs with high Tourism can cause unrest in civs using a different ideology where their culture is popular.
Also beware power blocs with lots of city-state allies, as they can pass a resolution in the World Congress instating a “World Ideology,” making it very hard for anyone outside that ideology to get anything passed ever again. A similar resolution exists for World Religion.
With the above suggestions in mind, you should be prepared to face the Brave New World that awaits you. Oh yeah, and Alexander is still a huge jerk.