JLPT N3 is the exciting level.
Things will make sense!
You'll walk past 7/11, glace at a sign and have to do a double-take because you know what it says. You'll open mail and think about who you can get to translate it before slapping yourself in the face and doing it yourself.
All this is only possible with the right resources, however, so here are our (well, my) recommendations.
There is one textbook series which only covers the higher levels (N3, 2 and 1), and which sold itself to me on it's simplicity.
It calls itself Nihongo So-Matome, and I recommend you buy the whole set.
There are five books, each covering one element of the test: Vocab, Kanji, Grammar, Reading and Listening.
Those of you in Japan, buy them all from Amazon (check the used section for some bargains - I got an N2 book for 171yen). Americans, I recommend you do the same. Brits, you're out of luck. If you don't like Amazon then I recommend White Rabbit Press.
The best part about each book is the presentation. I've used a few books before, and quickly gotten tired of the endless examples and questions. Nihongo So-Matome presents the information briefly and concisely, with contextual signs/packaging as a great bonus. Look at this example from the kanji book:
So you're pretty much on your own with the language learning. The book gets you going, but you'll need to roll up your sleeves and work out your own system to learn effectively.
If you want a list of practice questions then you'll need to buy the Ask practice books.
The books claim you can finish them in 6 weeks each (4 weeks for listening, which actually took me one 5-hour day), but really that's just a clever way to divide the information and set you goals. You can, if you have nothing else to do, finish all the books in a total of 6 weeks. Though I would recommend you budget around that long per book (including reviews).
I advise you study in this order:
- Vocab - get all this learned before moving on and it will be a lot simpler to understand example sentences, and memorise the kanji.
- Kanji - there are actually more kanji compound words than there are words in the vocab, so studying this next will give you some breathing space to accommodate those extras.
- Grammar - The most important book to master, but easier to do so with the knowledge of the previous two books.
- Reading - covers all the above.
- Listening - you can do this before the reading, but knowing the vocab and grammar is essential.
The best way to remember all these new facts and patterns is by using Anki (a free flashcard-scheduling programme if you didn't know). AND, lucky for you, I actually made cards for every page of each textbook as I studied them (which turned out to be more than 4,000), and uploaded them to Anki's server. See my entry on Anki decks to see how you can get a hold of these for yourself (free of charge, of course).
Now, these books aren't without their faults, as you will learn. Sometimes the grammar examples aren't quite enough to facilitate a full understanding. In these cases I found it useful to consult Tae Kim's guide or some other resource. Also, sometimes the vocab isn't clearly defined, in that new words will appear in sentences but not alone, so it may be difficult to pinpoint their exact meaning. Jisho.org answered all my questions there.