FreeCol is an open version of Colonization, a Civilization-like game in which the player has to conquer the new world.
You start the game with one vessel and two colonists. In the beginning you'll be able to send ships back to Europe in order to sell the goods you've produced or to bring back some colonists. Getting colonists into the new world is an important aspect of the game as each turn takes one year and later on even one season and as a result colonies don't grow as rapidly as they do in Civilization. You can pay colonists to come to the new world or you can attempt to persuade them with the religious freedom of your people in which case they will hop on your vessels for no money at all.
Another important aspect is trade, the source of all income apart from Inca and Aztec gold. In a land filled with precious resources it is important to build your colonies at the right location and to place crafstmen where they belong. This is not only to have an income but also to be able to live off the land when you can no longer count on the support of Europe.
Through all this you'll have to decide whether or not you want to live next to the native americans peacefully. They can teach your colonists new skills that cannot be taught anywhere else and they will offer you goods in case you choose to treat them as your friends. On the other hand, their villages can be attacked and their valuable goods can be taken from them and sold in Europe.
Other European forces are also busy occupying their piece of the new world. Should their borders go too far then take over some of their colonies by force because they wouldn't hesitate to do the same thing to you.
The object of Colonization is to declare your independence and survive an attack of the King's forces. Before declaring your independence you need to have the majority of the people behind you. This can be done by promoting free speech and by providing a strong governmental system.