So I gather you want to make an application that polls the Twitch API once a minute and then notifies when, say, followed channel is online?
Read about the Twitch API here.
C++ does not natively support http requests so you need an external library. This site provides examples with sample code.
You need an additional library to parse the returned JSON string, and another for the GUI and so on. I suggest you code this in another language, like Java.