See if the online radio service you're interested in has API documentation, which will have information about how to interact with their service. It's currently fashionable for web apps to use RESTful API's that are built on top of http, json, and oauth, so expect to see that kind of stuff.
As an example, (unofficial) Pandora API documentation:
https://6xq.net/pandora-apidoc/json/
Building an API client brings a lot of topics together into one project that most GM users would find pretty advanced, and it can be obnoxious even when you have the right tools for the job (ideally strong web programming skills, quality documentation, perhaps even a purpose built library). Every web service API has it's own individual quirks, and authentication can be tough to figure out. It's ambitious project to say the least for GameMaker.