The word I have always used and often seen in use for the internet is interrete.
The third declension neuter rete means "net".
A rete can be used for catching animals or fighting on the arena.
The prefix inter- is of course of Latin origin, so it makes sense to translate "inter-net" as inter-rete.
By analogy to the ancient net-fighter, I like calling internet users interretiarii.
Another natural derivative is the adjective interretialis, which can be used to describe a "web page", pagina interretialis.
The page in this context is clearly an extension of the page of a book, and pagina is the perfect word for that purpose.
If you want to refer to a network other than the internet, one option is nexus.
That word is often used as a translation for "link", though, so it might be confusing.
Perhaps the best general word for "network" or "web" is simply rete.
One option is to use the word tela (a spider's web), but I prefer interrete because the prefix reminds of the same word in other languages, whereas tela can be harder to grasp if you have never heard it before.
As always with technology, there is no single canonical correct translation to Latin.