The beginning of the game is the most crucial point. First of all, always start out as the Dutch, for as you will see later, it is more important to have advantages in funds and trade than in conquest, immigration, or cooperation. Always begin colonizing on the South American continent and the Caribbean. This has the best resources, sugar and rum especially. The colonies should always be right on the coast, so your ships have easy access to the goods. If, for some reason, you have to make a colony far inland, make a road to the nearest coastal colony. When you make colonies, always make sure they are defended by at least one soldier or dragoon. Now, simply start producing goods that are available, load them on to your merchantman (you will have one if you started out as the Dutch), and sell them in Europe. If you have followed my advice so far, you should have at least 7,500 gold by the year 1600!
First rule with the natives: Always remain in good standing. It will never be necessary to burn an Indian village if you play your cards right. When they ask for food, always give it to them. When foreign colonial powers attack them, defend the natives. This is all because if you are in good standing with the Indians in America, you can easily control the other colonial powers, and the foreign powers are not exactly nice to the Indians. When you arrive in an area where another nation has settled, the natives you meet will usually be very alarmed. If you want to weaken any other nation, send in a missionary to the Indian villages around the foreign colonies, and incite the Indians to attack the other powers. However, never trade guns or horses to the Indians! If you happen to annoy the Indians in the slightest, they will use them against you. Now a regular Indian brave unit might not be any trouble, but one armed with guns, or riding on horses? This is definitely a problem.
Handling relations with other nations is tricky, to say the least. If you say something wrong, or don't donate money to their church at a certain time, they might go off on some holy war against you. I recommend always staying at peace with other nations... publicly. Privately, you can wage war against them, without them ever knowing it, by making use of privateers. These units are extremely useful, especially for disrupting enemy shipping. They also have a variety of other uses, including blockading ports, transporting units, etc. Frigates are not a good purchase, since by attacking another nation with one of those, you are declaring war. It is also possible to push back enemy nations without attacking them directly. First find an enemy colony you want to get rid of. Then blockade it with privateers by surrounding the colony in question so no trade ships can get through. Then, land a missionary, and incite the local natives to attack that nation. Soon, the colony will either be abandoned or heavily weakened. If it is just heavily weakened, you might have to attack them directly once just to capture the colony. Then you must quickly make peace with that nation again.
The War for Independence
Before you declare independence, you must prepare your colonies. First, you must make sure that you have a lot of colonies, and that all are defended by at least one soldier or dragoon (dragoons are much better). This is to split up the main attack by your mother country. When they land they will either have to split their force, or concentrate a large number of forces on each colony, and conquer one by one. Either way, they're in trouble. If they split, you have an easier time destroying them. If they concentrate their forces in a large mass, then you can easily isolate them, and surround them. The second thing you have to do is keep a large amount of troops simply on land, and not base them in any colony. You also must have some troops on privateers as landing forces (now you start to get why funds and trade are more important than any other skill; the more forces you have, the better). You also must know the correct time to declare independence. If you declare too early, you may not be ready for the onslaught of troops heading your way. If you declare too late, then the enemy force will be overwhelming, since so many troops have been added. When independence is declared, and the initial troop landing has occurred, then you must attack it with your land army. Use your privateers to stop any more ships from coming in with more troops, or at the very least, delay them, so your troops can deal with wave after wave of the enemy. Tactics are very important in these battles. Don't just attack a mass of their troops with a mass of your troops just by charging them. Remember, these troops are probably better trained than yours. First, outflank them, so they are attacked from several sides. Then, wedge them, by charging their middle, and splitting their army into two parts. Then, destroy the isolated parts. Artillery can play a large part in battles, but only for hit-and-run attacks. Artillery can deal out some punishment, but it can't take very much. Protect your artillery! It is very valuable in this war, especially for taking back captured colonies.
There it is. If you follow these tips, you should be on your way to creating a new nation in no time.