A Gachapon is a lottery-like minigame that awards players with random items in exchange for Gachapon Tickets, which are purchased through the Cash Shop.
These can be found in the "Random Rewards" → "Gachapon Tickets" category of the Cash Shop.
There are two types of Gachapon Tickets. To use regular Gachapon Tickets, you need to visit the Gachapon machine found in most major towns.
Remote Gachapon Tickets can be used anytime by simply double-clicking the ticket in your character's inventory.