thedkm: I have already struggled to manage the new world and my army but thank you even for this advice.
some more tips ;)
Don't underestimate the experience, can make the difference between winning and loosing, although naval seems to be unaffected by it.
If you go to war, try to get the AI to join you when fighting against another AI.
The NW is mainly for resources, As mentioned above furs and similar. Try to get minor countries in the old world to join you. If you have a minor country on the same landmass as you, get them. What I usually do, I declare war upon them in the first turn, means even if they sign a treaty afterwards it will have no effect, you can conquer them without penalty later ;)
Only old world provinces do count for victory, theoretically you could win without taking any NW country. Always wanted to try, just to see if it is possible ;)
Also, try to do as much as possible with train. If possible avoid naval transport. Naval can be blockaded and if this happens:
a.) you might loose ships
b.) you do not get the resources.
Yes NW is only via naval. Hence important to get old world countries for the basic resources (and FOOD)
To defend, you do NOT need army everywhere. Normally you get a warning of a naval invasion. Pay attention to those messages (it tells you the province name), move your defending forces there and they will arrive in time.
One tip about building roads/train: Due to the above mentioned fact (improving cities), make sure that all resources in ONE province are being transported into the city of this province. Unlike CIV it has to be connected straight into the city and not just any road. Meaning, if the road collecting the resource is coming from another province (and not connected to its 'own' city) it will not count towards bonus production. But only interesting for resources which can have follow up products, so like sugar, furs, wood and similar. Money resources it doesn't matter.
Hence also be careful were you build harbours, they count as transport capacity 4.
Army: stationary artillery is good for defending, mobile for attacking. Always keep some units in reserve, meaning do not shoot them while it is your turn, this way if the AI will attack you they will run into your fire. Units behind fortification take less damage unless the fortification gets destroyed.
Attacking, you have two goals: Winning and destroying as much units as possible. Why? The units which can retreat will go back to another province and you will have to fight them later (again). Meaning IF you attack a nation, plan to win everything in one row, so that the enemy units can not recover from their injuries.
Also sometimes retreat is a good option. If you can not directly take a province because of fortification, keep in mind, if you destroy all artillery from fortification, the fortification will be downgraded one level, all what you have to do, get THOSE artillery into the yellow, stay one more turn that they disappear and than retreat. next attack you will face a fortification one level lower.
Hope it helps ;)