To find missing equipment for your hero's slots, enter their profile and examine those slots. You will learn where that specific piece of gear can be found. Replay previous levels and farm for required gear to complete their equipment set.
Free bonus chests
Open the silver chests every five minutes to receive items and equipment, and rarely a hero piece, as a reward. The gold chest can be opened for free every other day. It usually awards very rare items.
Heroes
Every hero has six equipment slots that once filled will allow that character to be promoted. During the process, that equipment will be sacrificed in order to give their stats permanently into that hero.
Skills
Heroes initially begin with only one skill, their active one. As a hero levels up by promotion, more skills will become available. These are usually passive skills that activate automatically. Skills can be leveled from the hero's profile page by spending gold.
Temporary buffs
Occassionally during battles, bubbles with icons will appear from defeated enemies. These are temporary buff power ups that can be tapped to activate. A maximum of two can be active at the same time. Use them generously, as they will disappear when the current level ends.