It goes beyond AT commands.
You use GPRS specific AT commands only to take up wireless link to the operator.
When you get “CONNECT” string from modem (terminal) the link is up and no more AT commands are used – PPP packages are sent and received.
Before you can send and receive IP packages form Internet, the PPP negotiations are carried out:
1. PPP LCP neg. packets are changed for most general PPP link parameters.
2. PPP PAP neg. packets are changed for login.
3. PPP IPCP neg. packets are changed for getting IP address, DNS etc.
When this process is done successfully then modem stops retransmitting negotiation packets.
Now you are connected to the Internet and IP packets can be changed.
Note that IP packets are also encapsulated in PPP packets.
PPP connection (GPRS link) is closed with PPP LCP terminate request.
This is basically how you connect embedded microcontroller device with RS-232 or COM port to the Internet using a GPRS phone, terminal etc.