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 using a supported USB-Ethernet adapter, you’ll also need James Peacock’s EtherUSB driver, which is included in the OMAP 3, OMAP 4, and Raspberry Pi ROM images.
If using an IOMD ROM based machine, the EtherB, EtherH, and EtherY drivers are available to download with the option to install the driver on disc or onto the expansion card itself.
Econet over IP is supported using the NetI module, which is included in the disc image. Simply activate this by enabling AUN from the !InetSetup dialogue.
The following online resources are currently available: