JLPT1: The 1kyuu
I studied for the 1kyuu from February 2008 until November of that year, and passed without trouble in December. In retrospect, if you want to work harder, and just prepare for the test, you probably don't need that much time.
If you just want to improve your Japanese, I'm not sure how relevant the 1kyuu is. Taking the 2kyuu is definitely worth it, but I'm not as convinced about the value of the 1kyuu. See why.
I prepared for the 1kyuu in basically the same way as I did for the 2kyuu, although for the 1kyuu I had significantly more time (one year instead of four months). If you haven't already, I recommend reading my thoughts on passing the 2kyuu, as the process is basically the same.
My Schedule of Preparation
I started early, which always helps. Since I started about ten months before the test, I could afford to have a leisurely pace. See my schedule in detail.
The Study of Kanji
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 (from my 2kyuu preparation) 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).
After finishing learning the kanji readings, as an additional way of review I started learning to write them. However, by the time I took the 1kyuu I could only write about 1000 kanji. As writing them was not necessary for the test, I only made a point of learning the ones that were difficult for me to remember. Also, since I already knew how to read them, and the common words that they are used in, then I didn't waste any time learning how to write kanji that are hardly ever used.
I tried as much as possible to get my day-to-day information in Japanese. At the beginning I used websites, as I could use Firefox and Rikaichan to instantly look up any kanji I didn't know, but as my reading ability improved I began reading the newspaper, as we always had Japanese newspapers laying around my office and there are few websites that match the quality of Japanese newspapers.
Throughout my 1kyuu preparation, I read books on topics that interested me in Japanese. This is the most relaxing and fun way to insure that you remember the kanji, and to learn new words. Since at the 1kyuu prep level one should probably already know at least one reading of most of the common kanji, it should be easy to look up words using a dictionary when one encounters them.
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 was not terribly difficult 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). The best practice for me was watching the evening news and listening to podcasts on my iPod during my commute to work.