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.