There were literally classes at the public library where people would get together and share websites. Also, because the web wasn’t monetized, similar sites would link to each other because they didn’t see other sites as competition for views and ad dollars. The Anime Turnpike, for example, was basically a yellow pages of any and all English-language websites related to anime. There were also “circles”* (even well after search engines entered the picture) of sites sharing a theme (eg a TV show fandom) and you could click through them like flipping through a Rolodex. But yeah, in the very early days (as in, before most folks even had email) word of mouth was quite prevalent; one of my mom’s favorite sites she heard about from a taxi driver.

*EDIT: Sorry, I got my languages mixed up; as others have said they were called webrings in English