Er, “travel to a place where the language is spoken” is nice and all, but it isn’t exactly the most low-budget option, folks.
In any case, “fluency” is a bit nebulous a term, but it is by all means possible to learn another language to the point where one can have intelligent conversations on a wide variety of topics, read books, watch films, etc., all without ever setting foot in a country in which the language is spoken. It simply requires practicing regularly, and making efficient use of the resources around you. And in Los Angeles, you should have quite a lot of available.
A few general tips:
Do NOT bother with formal classes. I’ve never met anyone who successfully learned a language with these without doing significant self-study on the side–and even then, they probably could have saved a good deal of time and money dropping the class portion and simply devoting more time to studying on their own.
Take advantage of your local library system. You’d be surprised what you can find here, often hidden in some far of branch (but easily delivered to a closer location) or in online form or somesuch.
Use the internet. Seriously, there is a TON of material here, much of it for free. It’s also a great way to meet native speakers, fellow learners, etc. The internet is the best thing to happen to language learning in decades.
Use a variety of materials. While you might focus primarily on one single “main” course at a time, it’s important to mix in lots of supplements as well. It’s just not possible to fit everything about a language into one book, after all.
Listen. Speak. Read. Write.
Some good “main” courses:
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Pimsleur: A pure audio course for beginners (and as a beginner, you want as much audio as you can get). A little slow and slightly repetitive, but for a first foreign language that’s probably a benefit. Definitely helps with pronunciation, as there’s no (or rather a minimal) text component, so you won’t be trying to match the sounds to those your brain tells you the letter “ought” to make. Stupidly high price makes it a phenomenal rip-off to buy in stores, but it’s almost certain your library will have it, at least for more common languages. Won’t get you that far, but what it does teach you, it makes sure you internalize.
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Foreign Service Institute courses: Created by the US government to train diplomats. Cheap-looking, but public domain. Mind-numbingly boring and insanely repetitive, but very, very effective. You WILL have a solid basis after finishing this–again, not complete fluency (no single course can bring you that), but an extremely good basis to build upon. Takes a little discipline to get through, but the rewards are high.
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Assimil: Never really used it myself, but a lot of people swear by it, including some accomplished polyglots. Certainly more entertaining than FSI. Based more on gaining an intuitive understanding than giving clear-cut grammatical explanations and following them up with practice exercises–a tactic which has both advantages and disadvantages. If you look for this in your local library, make sure they have the critical audio component (my own library system only seems to carry the books, for some reason). I cannot overemphasize the important of audio!
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Living Language “Ultimate” series: A more traditional approach which manages to be thorough without being boring. Lively dialogues, clear grammatical explanations. Most importantly, though, it’s one of the few contemporary series to continue to offer good courses for more advanced learners, rather than catering solely to beginners.
Once you build up a good basis, try reading newspaper and watching (or listening to) newscasts in your target language. The latter, especially, may seem difficult at first, and you’ll need to look up a good many words, but you’ll get used to it in time, and it will boost your vocabulary and listening skills by a phenomenal degree. After a while, you’ll want to start seeking out local conversation groups as well (libraries and universities are a good place to find these). Remember, nothing will improve your language skills more than actually using them!
Finally, don’t let yourself get discouraged. Sometimes you’ll run across periods when you don’t seem to be making any progress at all, and it seems a though no one could ever remember all these words and grammatical rules. But take heart. It is possible, and you can do it. Anyone can learn another language–it just takes dedication.
(Also–Spanish or Japanese? Those are on complete opposite ends of the scale. In any case I really don’t recommend Japanese as a first foreign language unless you’re really, really sure you have the drive to learn it. Your first language is going to be hard no matter what–but Japanese is just taking things to extremes, as it’s so completely different from English in every way. It is possible to learn Japanese without prior language experience–a very good friend of mine succeeded in doing so–but it requires some serious dedication, and I’ve witnessed far to many people giving up because they had underestimated its difficulties).