Heroes can be leveled up by gaining experience from battle or using training items. You can get the items as rewards from galadriel's gift, chests like the Hero's Chest, and in the shop.
To see the current level of your heroes and add experience, go to your great hall and tap on "Heroes".
Once at level 300, heroes no longer gain experience via combat or training items. You will then require a Hero's Glory or Hero's Renown.
- Hero's Glory: Will raise the level of your hero to the level of the item.
- Hero's Renown: Will raise the level of your hero by one.
The current level cap on most worlds is 300, except for Classic1, which is 225.