I have been studying for the 1kyuu since February 2007, when I found out I had passed the 2kyuu. Here I will share what I have done to prepare for the test, and if I pass, I will share the results and my thoughts on what is effective and what isn't.
I started early, which always helps. Since I started about ten months before the test, I can afford to have a leisurely pace. See my schedule in detail.
The 1kyuu requires significant ability to read and identify kanji. So, to begin my preparation, I decided to learn how to read all 1945 kanji that are taught in Japan through high school (nearly all of which can appear on the 1kyuu without furigana).
Learning the kanji is one of the most difficult things for native speakers of English. Thankfully, I found a real gem, the Kanji in Context series, which systematically teaches all 1945 kanji. Although I already knew about 1000 kanji when I started, I went ahead and started from the beginning, as the book recommended, and I'm glad I did. It took me about three and a half months of intense study, but using the books together with Mnemosyne I learned to read nearly all of the kanji, plus a few thousand new vocabulary words-- nearly all of which were from the 1kyuu lists.
I highly recommend these books if you have the time to spend with them. There are 143 lessons total, so if you do one a day, you will learn about 20 kanji, 40 words, and it will take about five months. I did it faster, but even at this relatively leisurely pace you should meet great success, as long as you're reviewing what you learn regularly (with Mnemosyne, for example).
Now that I finished studying the kanji readings, I'm going back and learning how to write them. Kanji I rarely see used I skip; since I'm reading books (see below), I have a decent idea of which are less useful now.
I try as much as possible to get my day-to-day information in Japanese. Rather than read the newspaper, I usually use websites, because with websites I can use Firefox and Rikaichan to instantly look up any kanji I don't know.
Just this year in time for the JLPT a fantastic book has been published, A Dictionary of Advanced Japanese Grammar. This is the third volume of the series, but you won't need the first two to get a lot of use out of this.
Like other grammar prep books, it covers most of the topics for the 1kyuu. What sets this one apart, though, is detailed English-language explanations and 5-15 example sentences for each point, plus translations in English.
Now, at the 1kyuu level I know most of us probably don't need English translations and furigana, but for the finer and demanding points of grammar all the analysis one can get helps, and here I find the English is a real asset. Of course, the book is a little expensive, but if you get it (assuming you already have どんな時どう使う 日本語表現文型辞典) that may be all you need in the way of explanations.
Unfortunately, since it was just published recently in Japan, it probably hasn't reached US bookstores yet. However, you can order it right now from Amazon Japan:
These days I'm reading books that interest me in Japanese. I'm continuing to practice the kanji as I read. Since I know nearly all of the common kanji now, it's easy to look up words I don't know on the computer, since I already know at least one reading for any given kanji. I will study the JLPT1 grammar later, but for now I've having fun reading what I want and improving my Japanese at the same time.
One book I recently finished that I recommend is Nikkei Ichinensei. The book is all in conversational format, and it explains basic economic concepts. If you know anything about economics you'll probably already understand everything in this book, but because of that, it's easy to understand and good Japanese practice. And it only costs about $7! (plus shipping, so get some textbooks too :)
Since I live in Japan, it's easier for me to get speaking and listening practice. However, since I teach English, it's not as easy as you might think (if you've never taught English in Japan). Some of my best practice comes from watching the news every night and listening to podcasts on my iPod.