You need at least one fort, over ten provinces, and an army by the end of the first year. You should also have laid the groundwork for magic with a cost-efficient research team and some site searching. To learn to do this, just keep rapidly starting new games against the AI and restart whenever you either mess up or succeed in your early game goals. Keep doing that until you don't mess up any more.
What an army means isn't as obvious as first apparent. Fighting independents you might get the impression that war is about morale and melee superiority. Your blob of infantry hits there's, one wraps around the other, and then within a couple of turns one of them routs. But against an actual human opponent, both of your armies will fill the entire width of the battlefield. Since units prioritize attacking horizontally over diagonally IIRC, this means each tile of infantry will only be hitting a single tile of enemies. Not good for a quick breakthrough.
So you need a way to do damage that isn't your frontline. This is where your mage support comes in (its mage support at first, at a certain point it flips over and your armies are supporting your mages). Your goal in the early game should be to pick a school and then have effective magic support for your armies using either the 4th or 5th level research of that school. Often in the second year one spell could be all you need to use, provided its a really good spell. What you tell your mages to use will define what kind of army you have. To make a very broad generalization, there are two types of armies in Dominions:
1. Armies which rely on ranged damage from the back line and use the frontline as a delay. This means evocation mages usually, but it could also mean fire arrow armies, or demons that have magic ranged attacks.
2. Armies that bias the battlefield in their favor so the front line wins a slow battle. This includes blessed sacreds, undead spam, fatigue causing globals, army buffs, probably some other things I've forgotten. The key point here is survivability; if you go up against the first type of army, you need to last long enough so that their evocation mages fall unconscious from spellcasting fatigue and their ranged units to run out of ammo. Usually this means having a vast HP pool and/or a lot of shields. If you go up against a flaming arrows army negating the flame effect is paramount, evocation mages generally only get off 3-5 spells but each archer will get at least a dozen shots and archers are cheaper than mages. Fire resistance is ideal, protection could be a poor substitute if necessary.
As the game goes on there'll be stranger and meaner strats, but for the most part its all one of those two. I'd recommend the first for newbs, but if you do want to try the second try to find a guide to narrow down what's viable for your faction. As the game goes on and you research more types of magic, most factions will start using both types of armies or combinations.
Also, if you want to go on the offensive in MP keep this in mind: wars are fought in two arenas: massing as much power into one province as possible (armies) and getting the most cost efficient unit together that can beat the enemy province defense (raiding). If you want to win a war, you need to be able to deal defensively with BOTH types of combat. If one side wins the army battle and one side wins the raiding battle, both of you are going to lose the game because neither of you has an effective defense against the other. Remember, even if the front is short they might have stealth or flying raiders so always be vigilant and always look up your neighbor's factions on the internet.