New World is a simple build map, in Fog of War games. In a 1v1 scenario, it's more than likely you'll wind up with someone rushing you, as is the generally accepted strategy. Normally, they first rush one of the three northern Indian homelands, depending on what they have. If you hold Aztec, chances are, you want to deploy Aztec, take Aztec 6, and than hold (while taking into account grabbing the European landing points, which you should always get ASAP). On the next turn, if they haven't come through, you grab Aztec 4 and 5, while deploying and sitting tight. Turn 3, they've usually either come through, or tried too, OR they're not rushing. In any case, it's normally time for you to go to them. Barrelling through Aztec 2 and Comanche 9, you have a straight shot at their Homeland.
Starting in Comanche or Inuit is the same deal, build and grab small bonus's slowly, and be patient. Mapuche is much the same, only you won't be leaving that place at all, if you don't hold Holland and/or Portugal to start; going after one Euro-Homeland and leaving yourself open to the other is a fail plan indeed.
Holding all Euro-homelands, your best plan is a rush. Take the landing point first turn, than rushing a Indian homeland is the best possible plan. The reason for this is, if someone holds all 4 or even 3 Indian homelands, he can easily take out all the 1's in the area, and have a 2nd Round bonus of 10+, minimum. So you have to act fast inorder to stop that.
In fog games, I just wait for them to come to me. Usually they think they're smart by getting a "huge bonus" and taking out the 4's and 6's in the Homelands and Euro landing points. However, that's the stupid thing about it; taking out a 4 to 6 person stack of neutrals to get a +1 bonus?