Sid Meier's Civilization IV: Colonization is both a stand-alone addon for Sid Meier's Civilization IV and a remake of Sid Meier's Colonization from 1994. So the basic premise of the game is still that the player becomes the Viceroy of one of the four playable countries (Netherlands, Spain, France and England) in 1500 with the goal to successfully declare independence from the old world and survive the repercussions in form of the Independence War before the year 1800 (although the winning conditions can be changed).
Based on which country and which of the two available Viceroys of that country the player chooses, he gets different bonuses and starts with different units on his lone ship in front of the shores of either a random generated map or a part of real America -- but the first goal is always the same: building a settlement at a good location. Based on which resources surround a settlement, it can harvest and produce different kinds of goods by the settlers currently occupying it. If enough food (200 units) is available, an additional settler will be available to work on the fields or in the different shops or be trained to become a master in his business and thus producing even more units per turn. These goods, for example cloth made out of cotton in the weaving mill, can then be traded with the natives or the other countries settling on the continent or sent back with a ship to Europe and sold there.
In Europe the player can also buy goods or hire additional settlers with or without specialization. Often, if the religious unrest in Europe is big enough, the people will come willingly with the player. This can be accelerated by producing religion points in your colony's religious establishments. Selling goods in Europe also means paying taxes to the king who will also demand additional payments from time to time, making it harder and harder for the player to please him, which increases the need to become independent.
But independence isn't something that can be declared at any time. Instead, 50% of the settlers in the new world have to agree with the decision before it can be made. And to get those 50%, settlers need to produce freedom bells in the city hall much like all the other trade goods. It is also very important to have a consistent policy with the natives, and the other countries because your handling of those relationships is critical.
Although the overall gameplay is still the same as in the original, changes have been made beside the better graphics and the addition of a multiplayer mode. One important change is, that military units don't degrade in rank when defeated but instead just die. To compensate this, a new unit known as the Great General has been introduced to the game. Once a unit has collected enough experience points, the Great General will spawn in a nearby settlement. Combining him with another military unit will then increase its combat strength significantly. It's now also not possible anymore for several nations to chose the same founding fathers. Once a nation has accepted Benjamin Franklin's help offer, he is lost to everyone else. A nation has to fulfill certain criteria (a certain number of points in specific areas like religion or military) before a founding father will even consider joining the nation.
Other changes include the addition of national borders much like in Sid Meier's Civilization IV which allow the player to conquer other cities just by expanding their culture border far enough and the possibility to choose a government style once independence has been declared and the constitution is drafted. A monarchical system for example allows the player to still trade with Europe, although the Independence War rages.