How would I add a page-by-page language "switcher" on a website, and should I - details...?

I have a website that I’ve nearly finished. It’s done both in English and Hungarian. I need to display an option for two language “choices” for the user. The simple solution to change languages/sites, is to put a link on the bottom of the pages to switch languages, and then just be bumped to the homepage of the site, in the opposite language. However, is there some sort of script that would bounce them directly to the page they are already on, just in that opposite language. Example: I’m on the Hungarian page for a “Events” section. If I hit the link at the bottom it would lead me to that exact page, just in English.

I know this is a very specific developer question, but if you were the user, would you even care which page swaps with which?