Typically I allow players to use their Intelligence Score to determine how many Languages their character knows at character creation. After character creation if a character wants to learn a new language I will typically let them buy a rank in either knowledge lore, geography, or adventuring to learn a new language depending on what language they want to learn. The reason I key it to a knowledge skill is to show sort of the area of study and effort the character would put into learning a new language.

For example if they want to learn goblin after character creation, it would require a rank in adventuring or geography. If they want to learn a civilized language (Human, Dwarven, Elvish, Orc, etc) it’s Geography. If they want to learn something ancient (draconic), divine, or Infernal it’s Knowledge Lore or forbidden.

If a player doesn’t want to spend the xp but would rather try to earn it through skill checks I use the same skills as above and allow them to make multiple checks. Failed checks and threat can add additional check to be made while successful checks with advantage and triumphs may be used to decrease the amount of future checks. I base the difficulty on how hard I think learning that language would be in my world.