The GSM (GPRS, UMTS etc) connection is lower level than the IP connection. So you need to make a GPRS or UMTS data connection from your modem to the operator's network, and an IP connection on top of that (usually both connections are done with one single connect command to the modem).
Then you can use this IP connection like any normal internet connection, and retrieve your json data.
How you make the GPRS/UMTS and IP connections, depends upon your platform.
As you are using C#, I guess it's Windows.
If the modem supports newer Windows interfaces, you can use Windows Mobile Broadband API on Win 7 or 8(desktop).
If the modem doesn't support Mobile Broadband API, then you can use AT commands. There is lots of help on the internet for that.