In addition to making the world Brave and New, Civ 5 's latest expansion can also make it a little confusing at first. With the huge changes to trade, culture, and diplomacy, you'll probably want to know a few things before you start shepherding your next civilization to victory. Listen closely, my liege...
Trade Routes are your main source of income
Before Brave New World, the main way to boost your income for most of the game was with buildings and, sometimes, tile improvements. Now, the new trade route system is what will be filling the lion's share of your coffers. If you want to get rich quick, research caravans (and later, cargo ships), and max out your trade route limit as early as possible.
Also keep in mind that trade routes are more profitable the more resources each partner has that the other doesn't. A wise Trade Prince will want to found cities on scarce luxuries for maximum profit. And don't forget to protect your trade routes from pirates and barbarians with a decent army and navy.
Tourism is thine sword, Culture is thine shield
The new method of culture victory involves overpowering the Culture of all other civs with your Tourism. If you're going for a Culture victory, this makes it important to get your culture train rolling as early as possible. But you were already doing that to stack those amazing policy bonuses, weren't you? Weren't you?!
If Culture victory sounds like your thing, be aware that you won't be able to generate a lot of tourism early on. Do whatever you can to boost your rate of Great Person generation, and rush like mad for the wonders that can hold Great Works with excellent theming bonuses. You will need to do some trading to make the most of said bonuses, but be sure you don't trade away something you're going to need for another slot later.