Training Your Partners
The first two sea mammals you find and can partner with in "Endless Ocean: Blue World" are the bottlenose dolphin and its cousin the spectacled porpoise. To teach them Level 1 tricks, you need to walk to the end of the pier on Nineball island and ring the bell. They will surface, and you must follow the Wii remote prompts to have them perform.
Gaining Levels
The easiest way to have your dolphins gain levels is to have them perform a trick until a message appears saying they cannot do it any better. Then switch dolphins and repeat. Once you have two or more dolphins at their training capacity, the game will reset so you can do it again, this time at Level 2. You can keep doing this until they reach Level 3.
Dolphin Shows and the Dolphin Levels
You will open up a mission titled "Be The Best Trainer" after teaching your dolphins a few tricks and getting them to Level 2. If you train them to Level 3, it makes putting on shows difficult because your dolphin may be requested to do Level 3 tricks and may fail. It is easier to complete the dolphin shows keeping your dolphins at Level 2, as they rarely fail at those tricks.
Dolphin Locations
As you play through the story, you will find missions like "White Dolphin in Ciceros"; you can recruit most of the special dolphins in these missions as partners. There are a total of 11 that you can partner with, so do not skip any missions with a dolphin or whale in the name. You will need all 11 to complete the "Be The Best Trainer" mission.