It looks like con 1 has TTL rs232 however there are multiple ports e.g. Port A and Port B
Also there is flow control on port A which you may need to loop back on its self for it to work.
On the arduino you will need to use software serial, as the hardware serial is already used to communicate with the PC
I'm not in a position to find the links, to the examples, so just google software serial Arduino and see how to setup the software and hardware to connect to another rs232 device
Remember that you need to connect Tx on the Arduino to Rx on the network board
Additionally you will then need to send commands to it, via serial
I don't know about this particular board, but the ones I have used, use an AT style command set like old fashioned modems
If there isn't an existing Arduino library for the AT command set that this board uses, you will have quite a lot of work ahead of you, to write library functions to do even the most basic of network functions e.f getting data from a web server, or acting as a web server etc
