I chose to learn the Japanese language on my own, and I don't regret it one bit.
Learning on your own is much more natural than learning in a classroom. Nobody learns their first language in a classroom, so why should they learn their second or third in a classroom? Further, I find many teaching methods to be rather inefficient, and
every teaching method is imperfect. When you learn in a classroom, you learn from a single person who has a single point of view based on a single set of personal experiences. Even native Japanese teachers. That pales in comparison to the extremely well-rounded approach of learning on your own from various books, websites and people. That allows you to weed out the language myths and misconceptions and receive a much broader impression of how the language is used and understood by different people in different places and situations. I also find that learning in a classroom usually becomes too serious and puts far too much pressure on something that should be fun, interesting and free. Learning on your own can feel effortless and enjoyable, whereas few classes can boast the same.
As far as where to begin, I began at the two following websites many years ago (thankfully they are still around!):
http://www.sf.airnet.ne.jp/~ts/japanese/index.html
http://www.freejapaneselessons.com/
The first site is especially helpful, as it gives a lot of insight for people who have absolutely no experience with the language or the culture. Even if you do know a thing or two, I'm willing to bet there will be plenty of useful and interesting info that you had no idea about.
Now you have to keep in mind that no one source is 100% accurate. Every Japanese-learning source contains errors or misconceptions, sometimes even glaring ones. It's best to take everything in as if it were
opinion, then gather other "opinions" and eventually come to your own view of how to use and understand the language. I promise that your skill with the language will be more well-received that way. I can tell you that from personal experience. I couldn't even count how many things I had heard or read that ended up being completely wrong. I also have a friend who took a couple of years of Japanese at the local university (from Japanese-born professors no less), and when he arrived in Japan for the first time, he felt as if half of everything he learned was outdated, inappropriate, or just plain wrong. You're going to get a little of that no matter what, but broadening your knowledge base will narrow that down considerably. The more sources, the better.
The most natural way to learn a language is through the spoken aspect first, as we all do with our own first languages. However, short of living in Japan with a family that will treat you as if you are their own young child, that isn't likely to pan out.
Much of your initial learning will be through reading. I recommend you check out many different websites and books. Try to vary your topical coverage. Once you begin to grasp
how the language works in its most basic aspects (the writing system, the pronunciation, etc), I would suggest first learning hiragana (and perhaps katakana). That will make it much easier and more enjoyable when it comes time to learn vocabulary. I found a freeware flashcard program that helped me to learn hiragana and katakana in several days. It didn't teach me how to
write the characters, but I could read them rather quickly, which I felt was much more important at this stage of the learning process.
Aside from reading, you will want to be able to listen to spoken Japanese as much as possible so that you can learn the speech patterns and just get used to hearing it. It is spoken much more quickly than English, and generally does not use emphasis like English does. If you are fortunate enough to live in a part of the world where you can access Japanese television signals (like much of west coast North America), then I recommend subscribing to said channels via your cable/satellite provider. Japanese television is very different from anything in North America or Europe, and gives a lot of insight into their culture and mannerisms. I highly recommend it if you can access it. I would gladly drop $100/month to add some Japanese television stations to my cable service if it were possible. I got totally hooked on it when I lived in Japan.
If you can't access Japanese television or movies, anime is the next best source of spoken Japanese, and happens to be very accessible throughout the world. Just beware that anime is saturated with slang and extremely far-reaching fiction, so it is probably best to use it as a tool of speech pattern reference, rather than as a direct vocabulary-learning tool.
Lastly, and perhaps most obviously, I highly recommend trying to find at least one native Japanese speaker with whom you can converse with for practice. Even if it is only an email penpal, that is far better than no one at all. That is what I did, as there are very very few Japanese in my city. Many sites online will match up penpals for language exchange, but you may want to spend some time studying before you venture into that area. I took the path of making a penpal after spending many months in self-study; I first wrote to her almost seven years ago, and it just so happens that now we are married! That shouldn't be your goal, of course, but stranger things could happen.
In a nutshell, try to immerse yourself in the language as much as possible. If you truly have a deep desire to learn the language and you enjoy the culture, then turn that passion into the energy it takes to motivate yourself to learn the language. Just remember that it will take
years; there is no fast track. Some ways are faster than others (like, say, spontaneously moving to Japan and learning by pure necessity), but don't try to rush it. Don't buy into any of those quick-learning gimicks. Be patient and the knowledge will come. It is always much easier to learn something if you have an interest in it, so try to enjoy the ride.