What languages can your character speak? Generally, that's up to you, but it should reflect your character's background in some way.
Your character starts speaking any languages that are included in your background in some way or another. For instance, if you were raised on a U.S. Military base in Okinawa, you might speak English and Japanese. If you've traveled extensively in South America, you might speak your native language, plus Arawakan, Spanish, and Portuguese.
Essentially, your starting languages are anything that makes sense. You can't just load up a bunch by adding "I'm multilingual" to your background - it has to be organic. If your character isn't multilingual, then don't take extra languages.
Once the game starts, learning more languages is handled through role play. The character needs to spend down time immersed in or studying the language. After sufficient time, they can speak the language.
A few things to note:
- learning languages is hard, but it's generally easier for people who are already multilingual
- learning languages related to ones you already speak is easier than learning completely different languages (if you speak Italian, it's easier to pick up Spanish than it is Cantonese)
- Being immersed in a language (you're living among people using it all the time, and your fumbling attempts at it are your primary means of communication) is the fastest way to learn it
- Some languages may be impossible to pronounce properly - extraterrestrial languages, for instance. A character might only be able to learn how to understand and/or read a language without speaking it
Characters are literate unless the player decides they're not. Depending on the campaign, this might qualify as a Tangle; depending on the setting and Parameters of a game, being illiterate might be a significant part of a character's background. A peasant in the year 1242CE being illiterate isn't a big deal, but being illiterate in 1980s England is a significant part of your character, and probably has a story attached to it.
You can fix being illiterate the same way you learn a new language (see above). When learning a new language, if you're already literate, it's assumed you're working on literacy in the new language as well.
You could also treat languages as Details, giving them some mechanical heft. Details don't really have a cost, so this doesn't alter much. You can usually only benefit from these Details if knowing the language would impress someone, or if the language is dead and/or especially obscure. This can help if you want to take a less ambiguous, more granular approach to languages.