Thanks for all the advice. I started a couple of new games, and finally stuck to one that really seemed to work out for me. It was a randomly generated map that (from what I can tell so far) has a large island, two smaller mid-sized islands, and a few small Hawaii sized islands. I was dropped on one of the mid-sized Islands with the Azteks.
I wasted NO time. I was near the shore, so I put my HQ right next to a mountain that had gold, some cows or something, and some trees. I immediately built a warrior and set it to build workers. I used my scout and my warrior and I scoured the entire territory as quickly as I could. I found several goody huts that really got me started (there were like 4 or 5 on the island, and they all gave me technologies).
I'm not ENTIRELY sure what I did too differently this time, but I built as many settlers as I could. While my HQ (Washington) was building settlers, I explored the entire island and found the Azteks. I refused to talk with them, and they declared war on me (but they didn't have any soldiers).
I immediately built a town within two squares of their capitol. I then built another on the other side of it, essentially trapping it in. They had built another city, but I conquered it with some soldiers and took it over. All they had left was a single city. After a few more turns, their old city (which I had captured) and the two that I built, had completely cut them off from the rest of the island. Unfortunately for them, their territory wasn't directly on the water either so they had no chance of building a ship. I decided that I didn't want to destroy them, so I made friends with them, and they're basically trapped in that one city.
I found a small waterway that would allow me to take my galley (first chance I had) and I found two much smaller islands (only a few squares really). There were goody huts on both of them, one gave me a town, and the other gave me gunpowder (I think).
I took my galley and found the big island. I then found the other Island, and it was the Chinese on there. I immediately put a settler down in the first open space I could find, and then constantly shipped Musketteers over from my home land to that territory. I built a couple of knights and sent them over too. I kept 4 Musketteers at the new city on the Chinese territory, and then took my 4 knights and several musketteers through each city on that map and decimated them (razing them). It took me at least a couple hundred years I think, but I ended up doing the same thing to the Chinese that I did to the Azteks. I surrounded their HQ with soldiers and then built towns around it. We're now friends
... but they can no longer expand.
There seems to be (best I can figure) two to three other cultures on the main land, but none of them are at war with me. I've started building on the tail end of the opposite side of the map where htey haven't been building, so I've been expanding there. I got navigation and built harbors as soon as I got the chance.
I've kept Depotism and maxed my research to as high as it can go. I don't know if I switched to Democracy or not at this point, but all my towns have banks, marketplaces, and universities. I think I'm drastically head of them as I can now move troops in army configurations (with the help of some guy that looks like King Arthur). I also have the Mirimack or whatever it is. Oh, I've also got electricity already, and it's only 1780 something... so America is definitely ahead of the curve now! About time!!!
I've got to destroy (contain) the other three groups now!
Looks like we have another CivFanatic in the making. Yes, there are a few more tips you will learn along the way, but you've already got some of the most important lessons: keep expanding and keep exploring in the early ages. Gradually, you'll get a little more efficient at war, and in peace. No rush, just keep having fun.
