The sole mini-game in Bleach: The 3rd Phantom will pop up at times in chapters after certain battles. It involves a straight path with items and status buffs along it, often with multiple exits on the top screen. The bottom screen shows eight potential people to talk to. The goal? To reach the goal point and have received multiple boosts from conversations while collecting items on the path.
Each character portrait has three bars below it. Each bar segment correlates to one block on Kon's path above. So if you plan carefully, you can collect items and avoid exit points. Most character conversations will cost between one and four blocks, but this can be reduced if you manage to land on a discount square.
Occasionally character portraits will also have icons on them. A heart means some sort of status boost. A treasure chest means you will collect an item. An exclamation point means important information and, most likely, further conversations that can be unlocked.
The information given by characters in the conversations isn't totally essential, story wise. So more often than not, you can choose who to talk to based on pure favoritism. Sure you'll gain extra insights or more information on characters, but if you don't speak Japanese, you don't have to worry about missing out.
Initially, the path for Kon will be short and there will only be a few characters with brief conversations. As the game progresses, you'll be able to be more sociable. More characters will appear, to the point where players will have to use the L and R buttons to shift to see more.
Just try to cram in as many conversations as possible, and try to collect lots of bonuses!
Images courtesy of Sega.