I think the documentation and the site is good, it even provide a "Try it out" feature to allow customizable the query string for testing on the document page.
mark as favorite: https://developers.themoviedb.org/3/account/mark-as-favorite
POST: https://api.themoviedb.org/3/account/{account_id}/favorite?api_key=<<api_key>>
get favorite movie: https://developers.themoviedb.org/3/account/get-favorite-movies
You just need a API key to make it work, where the API key can be generated at the settings page. https://www.themoviedb.org/settings/api/request
ANDRE MADARANG had a series that request IGDB api, I think it's quite similar to your app and may give you some ideas. https://laracasts.com/series/build-a-video-game-aggregator