You will encounter Ukulele Pichu on Dolce Island where it is leading a group of other Pokémon with it's music. It hides in the bushes when the Pokémon Pinchers show up to 'pinch' all of the Pokémon on Dolce Island. After it witnesses the capture of all it's Pokémon friends and spots you, it challenges you to a battle. All you have to do is capture it with your Capture Styler, and it will be your partner for the rest of the game, with Booker's permission.
Ukulele Pichu's Pokémon Assist
Like the other partner Pokémon, Pichu has a very unique Pokémon Assist. First, when you send it out to the field, it will play it's ukulele to send outdamaging musical notes that do little damage to your enemy. After that, Pichu does massive damage with it great electical charges. It's Assist can be upgraded as your styler levels up, just like other Partner Pokémon.
The only drawback to the Ukulele Pichu being your Partner Pokémon is whenever you go back or foward in time, Pichu stays behind. On the bright side, you are able to get new Partner Pokémon for the past and the future. Pichu comes back to follow you when you return to the present and in the present, you are able to call your other Partner Pokémon via Ranger Signs.