This is a pretty brief guide for the Scenario - Conquest of the New World.
This is workable in Emperor (Level 6) for me in all EU nations.

-As EU, fighting against each other is pretty much the last thing you want to happen.
-Your capitcal city is very productive, while land is limited by Japan, unreachable NPC, so growth is pretty meaningless.
-Your capitcal city will output the majority of your army in the mid-late game, like a Musketeer or Cannon every 2 turn
-The victory condition is reaching 1000 Victory Points before Turn 100.
-Depending on your map spawn, you may/maynot reach China (most western side), you'll need new Settler/Conquistadors to move to the West cost of America. The FIRST THREE CARAVAN reaching China will give you 200/100/50 Victory Points respectively.
-Conquering (non-EU?) city gives you one treasure, transporting them back to your capitcal city will give you 50 Victory Points each.
-Capitcal City of the Native American will gives you three treasure.
-Some Wonders you discover will spawn you treasure periodically.

Switch to Productive focus, Workshop -> Ironworks -> National Treasury -> (Forge-> Armory or any buildings you like) or directly go for building your army. You also want to utilize your citizen by putting on specialists, until your city is stagnant, as mentioned, growth is not necessary. This way you can also born a lot of great people for more productoin or Golden Age

Go either 2 Liberty (Collective Rule for Settler) and 1 Commerce, or 3 Commerce till Merchant Navy, depends on your playstyle. Liberty first give you a head start on building new cities, but it may slow down your progress down the Commerce tree. But somehow settling as fast isn't that important so it's your choice again.

I go directly for Cannon/Musketeer. Since I don't really fight naval battle so I'll leave navy development behind. If you have found a lot of luxuries and settled a few resourceful cities, you'll need to manage your happiness. This time you'll need to switch to developing Circus and Colloseum.

(You may want an armory in your capitcal which gives you two upgrade.) Solely building Melee+Seige units can do the job in the whole game.

-As Spain you'll want to open up the map as much as you can, earning gold from discovering Wonders.
-As UK, hope you can directly reach China through waterway.
-As France, City-state does give you little advantages but it's really limited. (Maybe I haven't fully utilize City-state function yet, feel free to tell me some :p)

-City-state doesn't matter much in my game.
-Rushing Cannon+Musketeer will let you crush any army in your way.
-Select your closest native to start with, ally with EU to war together or just the native with worst EU relation
-Before Delcare of War, you can cheat on them by trading everything for their gold, then break the contract by DOW, but you'll still receive the cash. Natives are very rich as well (2000+ gold), this method is not very moral though.
-You can settle some city, even resourceless, around the natives and trade them to the closest native, they may want to buy your city with decent cash.
-Spent most of your gold on buying units only on your American cities, with priority over your EU capital, as it takes shorter time to reach the battlefield. Unless you need some ship/cannon to defend your capitcal, or you're just too rich.
-Spent part of your gold managing your happiness, as well as building up your America city if it's resourceful.
-Again, often check and allocate the citizens manually to suit your need. Some are just too unproductive you need to grow it, some are too productive you want to sacrifice growth to produce more units or efficient buildings.

-Trade all their cash before starting war.
-(Slightly immoral, or just solely being commerical :p) Aim for their capital as they spawn 3 treasures. Then TRADE IT BACK to the native, you may want to buy it back so hard with tons of their resources. Having peace with them is acceptable, wait it out, capture it again.
-You might lack a bit of Victory Points to reach 1000 in the last few turns. Note that VP depends on City, Population, Land, Wonders/China, Tech and Treasures. If you're desparate, forget about the war, turn all your resources to build city, food focus and most important, buy every cheapest land you can afford in your cities.

This is my first little guide/tips and it's so far on the EU side only.
I'll update the native side sooner or later when I finish them.
So happy conquering for the time being :p

P.S.
You might wanna play in without those immoral trades so increase your fun, it's also playable but you'll need to handle much more politics with other EU nations.