I thought it wise to share the rulings that I've been using for these games.
The Common TongueAll characters speak their native language plus common. Common, as I see it, is not (nor was it ever supposed to be) the language shared by all humans everywhere. Rather, it is a general sort of mish mash, a patois of major human language groups, developed for purpose of trade and settle small differences. As such, it is often difficult to get across complex ideas or highly representational thought without recourse to another language; common just doesn't have words for these things that share enough commonality amongst its constituent language groups, and so there are just some things that you can't explain in common. This makes it important for PCs from different places to learn each others' languages (and it gives folks a reason to bother learning, say, dwarven [duersku] or elven [alvlantesk], despite the fact that dwarves and elves can typically speak common).
Initial LanguagesOther than their native tongues and common, characters may choose a number of languages equal to whatever their particular rule set suggests is appropriate. ACKS gives players 1 additional language per point of Intelligence bonus (as does DCC, twice as many if you're a wizard). Delving Deeper has a nice chart that tells you how many languages you may know, but it is inclusive of the native tongue and common (thus, you get one additional language at 11, two at 12, and so on according to table 1.3). These languages are typically chosen from a list of "highly relevant" languages, but may be rolled for if the situation (or DM dictate) warrants. I try to have a list of the high relevant languages on hand when characters are being created, but will readily admit that I don't tend to keep it around for long afterward. (Blog post inspiration!) Demihumans get no special "racial languages" beyond their native language; instead, they learn to communicate very simple ideas. Think about the snippets of language you learn when going to a foreign country: enough to attain needs, be polite and (often) be rude.
Unassigned LanguagesWhen creating a character, a player does not need to assign all of his available "language slots." In fact, for my Hyperbarbaria game, I didn't let anyone choose any additional languages, but for my Iron Coast campaign, several players choose to keep language slots open. Instead, these "open slots" may be spent later on to learn a language to which the character has been exposed (immersion learning) or to chooses to study (the ol' fashioned way). The exact system for how to do this is kind of up in the air, but here are some options:
Carousing?I love carousing rules. The opportunity to waste hard-earn gold for material gain is a great thing. By this time, I feel like it's common use of the term to suggest that, for the murderhobo of a character your PC is, "carousing" might apply just as readily to feasting and getting drunk with the locals as to finding a tutor to teach your character a lost bit of lore, to spending vast amounts of money in an attempt to woo a particular would-be paramour. Learning a language is another perfectly logical way to spend that money and time. The DM should set a goal for how much money will need to be spent in this manner and the player is in charge of figuring out where that money goes. Language tutors. Phrase books. Rounds of drinks for native speakers of the language. Stuff like that.
To set an arbitrary amount, how about 50 gp times the number of languages currently known, possibly multiplied by the PC's level, depending on how onerous you want it to be. That works for me.
Total ImmersionSometimes, the PC will not have recourse to tutors or other resources to help him blow his gold on learning a language. If, say, your ranger were captured by vermen and, somehow, did not yet speak the Black Speech, he might learn their particular dialect by observing and mimicking what he observes. At the end of whatever time the DM sets, the player may make a 2d6 roll for his PC, adding 1 for each score in Intelligence, Wisdom or Charisma of 15 or above, subtracting 1 for each of those scores of 7 or less. If the PC has a partner or tutor to help him practice the language, he gains an additional +1 bonus, but if he has been unable to practice at all (and is just learning from listening), he takes -1 penalty. If the roll is 6 or less, the PC fails and may try again after the same interval has passed. After the third failure, the PC may not try again. If the roll is 7-9, the PC succeeds, but either his comprehension or speech is imperfect (perhaps he has a strong accent or the like). A 10 or better is a complete success.
Again, lets set some arbitrary time frames. One month times the number of languages already spoken, possibly plus the PC's level in months, again, depending on how tough you want it to be.