RISC OS is an Operating System which has (always?) supported networking. From Econet to Access and AUN (Acorn Universal Networking), there have always been ways to connect RISC OS computers together. Use of modems (historically) and ethernet connections facilitate connection to the internet.
Information on basic networking descibes some further background.
If your hardware isn’t fitted with an ethernet socket, you’ll need a compatible USB-Ethernet adapter. Such an item is listed in the Cortex-A8 hardware compatability list?.
If using a USB-Ethernet adapter, you’ll also need James Peacock’s EtherUSB .
The following online resources are currently available: