After your modem configuration, you need to implemente PPP protocol, TCP/IP to connect to internet.
The Point to Point Protocol (PPP)
On this site, you can find a good description of PPP packets for initialisation.
I have a similar project, and i am on this state. But i have a lot of problem.
I use C source that you can find on this site :
SourceForge.net: uC/IP - TCP/IP for microcontrollers