There are a few ways to obtain items.
- rewards from blue portals
- enemies can randomly drop them
- treasure chests on the battlefield
You can equip items or remove items only from people who aren't out in the field or currently returning from the field (yellowed out). Gold backed items are the best in size to power ratio. Everything except green backed items can be reduced to a smaller size, but it requires gold to reduce them. Drag an item and put it below the row of items. A blue bar will appear and that will shrink them. Costs 100 for 5x5->4x4, 200 for 4x4->3x3 and 300 for the last one. Gold can also be obtained when you drop the items into the void (where the character selection area is on the item screen). The amount is listed in the item information box down below.