As you complete the various missions on offer you will begin to gather a collection of gear your characters. To view what new gear you can equip your characters you must go to the roster screen where if you see a green plus sign beside any of your heroes or villains it indicates that an equippable item is available for them. The best strategy is to just focus on equipping the characters that you take into battle on a regular basis. Once you have filled all six of the equipment slots for a character you will be presented with the option of upgrading them to the next tier which will make them more powerful.