After you get a feel for Dominions, you forget how lost you were at first, and how all the "obvious" strategies are not, in fact, obvious; but rather things that other people told you, and you never would have figured out otherwise.
On of the most important things to know is, that the AI will always attack the weakest defended province. I usually leave one province without PD, so I know it is this province that will be attacked. Whenever an enemy army appears, I command my forces to move into that province to intercept. This works 99 percent of the time, and prevents the enemy to rampage through your provinces