This is how I play the game:
My goal is to be the *first* power to gain indepencence. I focus on small empire with good machinery to produce armed force. The end game is the goal that should always be in your mind when playing.
EARLY GAME: getting a good start.
- search a good coastal place for first colony. My first priority is food and production. then ore. then other goods.
- to get a good start, you need people fast, and if they are professional, the better.
- send some scouts as soon as possible to get every lost city piece and visit every indian village (you get something from almost every village, and especially from aztecs and incas). See what professions they train. Sugar/cotton/tobacco planters can be gained only by indian training (random learning from working also, but it is too rare)
- try to find silver at the _early_ game, you get LOTS of money! In the end game it is almost useless, so be quick!
- at start, just sell something to get money for people (to get fast start)
- at start, it is sometimes wise to hurry immigration by buing them at Europe. You probably cannot "train" expensive professionals at start.
- buy tools, muskets and horses at early game (I helps you to get started, and they will get more expensive later)
- trade some trade goods with indians at start. You get good money. It only works few times, later it is not useful.
- the first building should, of course, be lumber mill. The others depend on the role of the colony.
- at start it is wise not to build big armies. It is better to make those people work rather that stand useless.
Do it as long as it is safe.
- for early game, Peter Minuit, William Brewster, Hernando de Soto are good ones. Maybe Sieur de la Salle.
MIDDLE GAME: establishing a strong production machinery.
- find some other colonies. It is best to have only one coastal colony (easy to fight the independence war) The good amount of colonies is 4-7. If you produce too much goods, their price goes down. Find colonies in places with lots of food, lumber and ore.
- Get a professional colonist for every work place.
- Start liberty bell production early to get production bonuses. Churches,catedrals and preachers are not very important in the game.
- There is no much point fighting with other powers. Defence yourself when attacked. You can also capture their soldiers when they lose their horses and weapons in fight. It is a good source of men.
- trade other goods with indians if you happen to find good deals. I have never found mission in Indian villages very big deal. Establish them if a jesuit missionary happens to appear in european docks.
- build your colonies to produce arms and goods.
- Accept smallest taxes, hold tea parties for the biggest ones (8% increase etc.)
LATE GAME: building army
- You aim is to get lots of men, horses and muskets. Breed as many horses as possible. Also build artillery.
- Some artilleries can be bought in Europe, but the price gets higher and higher. Recruit some people from Europe, capture from foreign powers and let your population grow.
- You can train ore miners for 600 at europe, clear their profession and train them in college/university.
- You can use indians to train your soldiers to veteran status. (George Washington is nice, if you happen to get him)
- slaugter at least aztecs and incas for money and for training your troops to veterans.
- build fortress in your costal colony and put LOTS of veteral dragoons and artilleries there.
- you don't really need much navy. Don't concentrate to it.
- Store extra horses to wagon trains, ships etc.
- If you have lots of money and little time, you can buy veteran soldiers (2000 gold!) from Europe.
- Also buy lots of horses/muskets/artillery from Europe if the price has not grown too much.
THE WAR OF THE INDEPENDENCE: finishing the game
- your should now have lots of veteran dragons and artilleries in your capital colony fortress. The continental army always attacks your only coastal city.
- Do not move your artillery anywhere. Fortify them in your fortress.
- Use dragoons to attack from outside of your colonies to get the cool terrain bonus.
- try to kill them at the same turn they arrive in your lands to prevent their HEAVY artillery attacks.
- do not attack on foot. equip your routed troops with horses as long as you have them. Horses are cheaper to replace than muskets and dragoons are deadlier.
THE END: aftermath
- wonder how easy it was to fight so big troops with only some (15 to 35) of dragoons and some artillery.
Big post
should I instead write "yet another strategy guide for Col"
She's exterminating natives! Shame on you!! 
Perhaps the converts would help me, but when you've only got three or four colonies and you haven't got any room for anymore colonists, the natives just tend to feel...unproductive. And I can't have natives trailing home without a taste of that old time religion. 
At least 6K gold... And if your converts are unproductive, you can make them soldiers 
