The MetaMask browser extension supports new translations added in the form of new locales files added in app/_locales.
Each supported language is represented by a folder in app/_locales whose name is that language's subtag (look up a language subtag using this tool).
Inside that folder there should be a messages.json file that follows the specified format. An easy way to start your translation is to first duplicate app/_locales/en/messages.json (the english translation), and then update the message key for each in-app message.
That's it! When MetaMask is loaded on a computer with that language set as the system language, they will see your translation instead of the default one.
To verify that your translation works, you will need to build a local copy of MetaMask.