How can I change the language in Pokémon GO?
For Android, Pokemon GO appears to use your device's set language.
In order to change the game language, you need to change the language of your phone.
For iOS, you will need to use Jake's answer.
I live in Japan and the app is in Japanese with my phone being in English. Unfortunately, I think the only way to change the language on iOS is to create an Apple ID in the country that speaks the language you want to use and download it from that App Store.