Welcome to the forum!
One tip you might find useful is not picking Vanheim, Helheim or Tir na n'Og as computer opponents when you start learning Dominions. They have a nasty habit of being able to mass absolutely humongous armies and they have some seriously good units, especially the heims. They don't lose too many of them in most battles, which means their units rack up experience, making them even tougher. Choose somewhat easier enemies to go up against at first, such as Arco, that will allow you a shot at winning.
The heims are by no means invulnerable or anything, but you need to know what to do to counter them.
Take a look at the various guides on the forum, especially Baalz's stuff is eye-opening, bu maybe a tad advanced for a beginner.