Armies can attack each other when they are adjacent to each other. This generally means they occupy adjacent hexes, but sometimes a unit may have the ability to attack from more than 1 hex away.
In the fiction, an attack means the attacking army is attempting to occupy the hex of the defending army. Any player may choose to attack with any army they control on the map, even if their commander is not a hosted by the army.
Rolling an Overworld Attack
When you attack with a unit, you attack either as its commander (your commander unit is hosted by the army), or as the player issuing orders from the overworld. Each unit has a single attribute value. Roll a d6 and add the unit's attribute. Whoever rolls highest wins the battle and deals 1 damage to the attacking unit. Ties mean that neither army has made inroads against the other, and no damage is dealt.
If the defending unit has 0 HP, it is removed from the map and the attacking unit may immediately occupy the hex of the defending unit.
Applying Related Skills
How you apply skills to an overworld attack depends on how you are controlling your army at the time of the attack. When you are attacking with an army that is not hosting your commander, you're issuing orders from afar. In this context, you cannot apply a skill or story tags, but you can use any narrative advantages created in the overworld and benefit from any abilities or bonuses provided by attachés.
Attacking as the Commander
When your commander unit is hosted by the army you are attacking with, you may rationalize the use of any skill that makes sense in the context of your being physically present to command your army. The skill must align with the attribute of the army you're commanding (Mighty armies respond to Mighty expertise, and so on.)
For example, you might use Influence to raise the morale of your troops with an inspiring speech before going into battle. You might use Culture to educate your troops about the social practices of the enemy and exploit their fears. You might use Nature to help your troops fight in a terrain you’re intimately familiar with.
Additionally, classes or kits that provide broad advantage in certain contexts can help justify the use of a skill that might otherwise not apply: the Warden's heightened recovery in wilds of their choosing, for example, could justify the use of Nature if the army is fighting on familiar terrain.