Back in September 2009 I started studying Japanese at SOAS, in the Beginners Certificate Course. This is an evening class with one two-hour lesson a week. Prior to joining the course, I'd tried to study at home, but found that I didn't have enough momentum to learn at the pace I wanted.
The course at SOAS uses the Minna No Nihongo books, which use kana (Japanese script) rather than romaji (latin script). This meant that those taking the course were expected to be familiar with the hiragana and katakana scripts before starting the lessons.
To learn this, I used a small book of mnemonics which helped me to learn the two basic Japanese alphabets: Kana Pict-o-Graphix: Mnemonics for Japanese Hiragana and Katakana. The book's about the size of a pad of post-it notes so it fits easily in a pocket, but the contents are invaluable in learning to read non-Kanji Japanese (which is most of what you'll encounter when you start learning).
To revise what I'd learned, I used the Kana Flip application. This is a flip-card app, with the added feature that it manages the order of the cards it shows you to maximise your chance of recalling them. Between this and the book, I managed to get to grips with the kana in about a week. I also used Kana Strokes to look up the characters and stroke order, and Kana Pad to practise them.
Having got the hang of the letters before the course, the next requirement was to start learning the vocabulary. There's a "Japanese Flip" application in the same family as Kana Flip, but it's less useful for the beginner as the smallest vocabulary set has 415 words - too much when you've only learned 20 words, and it's not possible to make your own lists on this app. However, once you get a bit further in, it becomes more useful.
If anyone does know an iPhone app that'll let you do this, please let me know!
One app I did buy early on was the dictionary app just called "Japanese". What I hadn't realised until recently was that this also lets you make your own word lists from the dictionary, which, while not as useful as flashcards, could still be helpful for vocab practice. This app is also very good for giving the stroke order for Kanji once you start using those.
It's worth noting, by the way, that the iPhone's actually quite good for entering Japanese text once you turn the right keyboards on. (Settings - General - Keyboards - International Keyboards - Japanese - Kana).
Once you move onto learning Kanji (in the second term in the SOAS course), other resources become useful. One book that's worth reading even before you really start on Kanji is "Read Japanese Today", which derives indirectly from the Shou Wen lexicon created around 200AD, but is an extremely interesting and readable book that makes 300 of the more common Kanji memorable by explaining their origins. There is also a "Kanji Flip" app that works much the same way as Kana Flip and Japanese Flip.
It's worth noting that, whatever language course or material you follow, you'll meet the vocabulary in very roughly the same order, as there's a standard Japanese Language Proficiency Test which groups the vocabulary into levels. So, pretty much all the vocab we've met in the first two terms of the SOAS course is in JPLT level 4, the first set in the Japanese Flip app.
One other lightweight and fun resource for early vocabulary is the Usborne "First Thousand Words in Japanese" book - I had the French version when I was about 10! (The Japanese version does have a couple of errors in though).
One thing you'll find, in a repeating head/desk way, while studying Japanese, is that Japanese grammar is incredibly tricky and very different from english grammar. The grammar covered in the SOAS course sometimes feels a bit lightweight, so I've looked for a few resources to help with that. Simply googling the relevant terms can be useful, but I've also found Yuki Johnson's Fundamentals of Japanese Grammar to be very readable, although it will occasionally leave you muttering to yourself about "Stative transitive predicates".
That covers most of the academic resources I tend to use. Outside of the classroom (and for that matter home study) there are a few useful locations and events for those of us in London: Grant and Cutler, Foreign-language booksellers and the Japan Centre's shop are both good places to browse for books, manga and media, and the Japanese Meetup Group is a very social event for those who are a little more practiced in the language.
The real-world shop at Japan Centre is incredibly hard to find (it's not where Google Maps says, for a start); it's on the extra bit of Regent Street everyone forgets, just south of Picadilly Circus. It's also not very good at all for books! (great for groceries though!) However, it's next door to Mitsukoshi, a Japanese Department store, and in the basement of Mitsukoshi is JP-books, which has thousands of books in Japanese.