I would like to know how I can retrieve the list of people a user is following on Instagram. This is given that this particular user is someone that I follow. So I have access to his/her photos and his followers on the Instagram app.
How can I use the Instagram API to do this? Is this legal to do?
Shiva's answer doesn't apply anymore. The API call "/users/{user-id}/follows" is not supported by Instagram for some time (it was disabled in 2016).
For a while you were able to get only your own followers/followings with "/users/self/follows" endpoint, but Instagram disabled that feature in April 2018 (with the Cambridge Analytica issue). You can read about it here.
As far as I know (at this moment) there isn't a service available (official or unofficial) where you can get the followers/followings of a user (even your own).