There is extensive discussion of AlphaNet (the Internet in Alpha Complex) in the appendix to Extreme PARANOIA. The forthcoming supplement Service, Service! supplement also discusses AlphaNet in its appendix, in a slightly different context.
First, know that any GM can have a different version of Alpha Complex, The Computer, etc., so the internet can be handled in many different ways. In my versions, AlphaNet is ubiquitous--it's hard to say where it ends and where other media and telecommunications end.
Troubleshooters use their Personal Digital Companions for c-mail and web browsing all the time, and so would other citizens. Service firms have their own websites, and much of the onipresent paperwork and forms are now digital and available online. But all of this is simply a tool for the GM to move the story along and have fun with the players.
I guess the simplest way to put it is this: the internet exists but only upon the whims of the GM in order to make sure the game session is entertaining.