To equip a weapon, go to your “Great Hall” > Heroes > equip > you should see a weapon on the bottom of the UI.
Drag and drop it into the weapon slot (below the avatar of your hero).
The same goes for other kind of gear, rings, amulets, shields, armor etc.
So far the game is giving players a free sword called “Arborist’s Weapon”.
You better equip it on your hero that has the highest level.
This sword gives 300 more attack and 100 more life.