To equip a shield, drag it to your left arm, not hand.
When equipped on the left arm, shields can block a large number of melee attacks against you. Shields damage very quickly when in use, so check and repair them frequently. When in combat, the option to shield bash an opponent will also be available. If successful, this will cause them to briefly be knocked over, reducing their defense for a short time.
Your skill in shields helps you block more incoming attacks and the shield will take less damage from use.