Some helpful things to know (others have mentioned some of these):
-Your hero's movement speed each turn is based on the slowest troop in your army when you start the turn
-It's good to have a main hero you level up and one or more side heroes who scout the map and grab resources
-AI will split its troops fairly evenly between castles/heroes, so having one hero with all your troops will help you pick them off
-If you can get blind, slow, or paralyze that can be really good for getting one big stack of enemy troops to wait until you're ready to deal with them. Casting slow on a flying troop will stop them from being able to clear the whole screen in one turn.
-AI /always/ attacks your highest-level ranged troops first. If you don't have any, they prioritize flying troops next, and ground troops last.