"where would someone have learned how to do that"
Call Demon and ask. They had the best tech support in the business.
"and obtained a command line browser that ran on Windows 95?"
As of August of 1994, Redmond was shipping "Wolverine" for WfWG, that included a TCP/IP stack (so-called "winsock") and command-line FTP program. It was included with Win95.
So to answer your question, dial up to Demon, and ftp lynx from the University of Kansas. Simples.
And yes, that's exactly what Demon support would have suggested in 1995 ... although it seems to me they had their own mirror of the Kansas site running on ftp.demon.co.uk/pub/ku/lynx ... failing that, I know for a fact that it was available at a SunSITE mirror near you.
"Perhaps by connecting to one of the online systems"
The OP already was connected to Demon.
Biting the hand that feeds IT
