The short answer is yes you can.
For hardware, you would need an ethernet card to connect to either a cable modem or DSL modem. The version of DSL modem available to you depends on the area you are in usually. In the US, if you request an ethernet based modem, they will give you one, but otherwise you'll wind up with a USB modem which would need drivers. The ethernet card should come with a networking software of some type. My Ariadne II card came with Genesis, and I've got it connecting my 040 based A3000 to the internet through my Cable modem and a Linksys router. Works great.