Under normal conditions, you can declare a Normal Attack with 1 of your monsters in the Dungeon by spending 1 Attack Crest from your Crest Pool. If you declare an attack through the effect of a monster or an item, you don't have to spends any Attack Crests.
In addition, there are certain monsters whose effects will require you to pay Attack Crests for their activation ("Knight of Twin Swords", for example).
Monster Lords are invulnerable to the effects of all monsters and items in play, which means that they can only be destroyed in Battle. When you don't have any Attack Crests in your Crest Pool, you're completely unable to defeat your opponent.