These items may only be dug up while on a Chocobo. They may be found by tracing the path of Goblin Diggers in the areas they are found in. If allowed to continue on their path without aggro, they will occasionally stop to bury an item. Wait for them to move on, then dig at the spot the item was buried to retrieve it.
Bear in mind that many of these items may also be purchased (from NPCs or other players). In some cases, a few may also be obtained through Mining or Excavation. Buying these items will be a less time-intensive method for completing the quest, though they can cost more than the reward you will obtain.
Trade a stack of eight of one type of item to Orlando. (He will only accept items in stacks of eight.) Rewards vary by the type of item traded: