Static HTML sites don't make this easy
You could have a Javascript that selects blocks of text and changes the text based on someone's language selection, but you'd have to custom code every piece of text or build quite a complex system of naming blocks of text and matching each block to a translation entry.. that's not impossible but is kinda a big job (I don't recommend this)
Neopets works using PHP, which means the pages are programaticly generated based on your preferences, that's a totally different technology (and it would still require quite a bit of work to setup; worth it for a complex site but not a small one).
If the translation is a primary focus for ur site then the best solution is just to have separate HTML pages for each language version of a page, make sure they all use a standard structure and use shared CSS to theme them all ^^ That not much fun to do, but its the best static solution. You can speed it up a lot if you use a static site generator like
11ty; 11ty takes a bit of learning, but I would say it's worth it if you have many pages and it's a good way to handle this.