How Can I Add The Languages box on my wiki?
Fragment of a discussion from Project:Support desk
That's just implemented as a normal template, with normal links (by hand). See Template:Languages for details on how that's implemented.
Technically you can have lang interwikis (aka lang links in sidebar like wikipedia) pointing to the same site, but it'd be a little weird (lang interwikis can point to any url, including the current website). See Manual:Interwiki#Interwiki_links_to_other_languages for details on how that feature works.
