You have this in the Mac Laptops category, but it's not a Mac. This laptop is running Linux.
The Elonex ONEt has wireless Internet connectivity. That means you can use a wireless router in your home in order to use it online. If you already have one, the system should be able to set itself up to use that connection on its own when you open a web browser. The web browser on your system is BonEcho/Firefox.
Another option is to run a Cat5e, also called an Ethernet cable, line from a router (or from your cable modem or DSL modem) directly to the laptop, since your laptop also has an ethernet port. This looks like a regular phone jack, but it's a little bigger.