I still don't have a great grasp of the language, so I'm not the most qualified to answer this, but this site
helped me get a basic grasp about the grammar and sentence structure. You'll also need to spend some time learning the alphabets. It's a bit complicated, but I'll give a quick rundown.
There's two phonetic alphabets, hiragana and katakana. Each has about 50 unique characters, each representing a specific sound. You're going to want to learn these alphabets first before you do much else, because you won't be able to get far without them.
After hiragana and katakana, there's a symbolic (that's not a technical term) alphabet called kanji, which consists of thousands of characters that each represent a different idea or object. You don't need to beat yourself up about learning these right away, but don't neglect them either, they're essential to reading and writing.
For learning the hiragana and katakana I just looked at some charts and memorized them after a couple weeks; there's not too many so it shouldn't be difficult to just drill a couple a day.
For the kanji, I originally used James W. Heisig's Remembering the Kanji
. It gives meanings to different "primitive" characters that are used to build up the more complicated characters, then uses those primitives to create a mnemonic you can associate with each character. It works great, but the copy I was using I had rented from the library, and I had to return it when I moved (ironically, I started taking my study much more seriously after I left Japan). I looked around to see if I could buy one, but everyplace I looked was either out of stock or wanted to charge $70+. Now I'm going through Kenneth G. Henshall's A Guide to Remembering Japanese Characters
, which I found for about $20. It uses a similar method, but the mnemonics it uses are a bit more "refined" scientifically. It goes over the history and evolution of each character, then uses this along with primitives to create the mnemonic. I find that both books work good, but Henshall's might be a bit more difficult in the beginning because some of the mnemonic's he provides aren't very usable, so you have to fill in the gaps yourself and make your own with the information he gives you. Also, while both books teach the meanings of each character, neither is very good at teaching the pronunciations (Henshall's book tells you what the sounds are but doesn't offer any learning aid, and Heisig's doesn't even mention the sounds, although they are covered in a second volume).
If possible, see if you can take a class as well. Even if you find that you study better on your own, it helps to immerse yourself, and in a class you'll be better able to do that, hearing what the language is supposed to sound like. Plus, if you get stuck you'll be able to ask for help from other students or the teacher. And don't just look at textbooks, use anything you can find. Web posts, children's books, random tattoos, imported movies, any practice helps. I had an advantage in this regard since any walk outside provided a chance for me to use my skills, plus trying to copy people I heard talking on the streets and in stores really helped my accent. But even outside of Japan, just a google search should give you plenty to practice with.
So yeah, there you go. Sorry that was long and ranty, but I hope you found some useful information. Oh, and one more thing, it doesn't hurt to listen to them, but don't try to learn Japanese from anime. There's a lot of weird over-the-top speech patterns that would get you laughed at if you tried to speak that way in real life.
EDIT: Grrr, TakaJun posted while I was writing this long post of mine. I need to paraphrase more.