I was recently asked how I learned the Japanese writing system. Actually, there are three: hiragana and katakana, which are phonetic systems, and kanji , which are basically Chinese characters embedded into Japanese text and pronounced as Japanese words.
The answer was that I was really bored the summer before I started high school, and had no qualms about butchering the English or Japanese languages. I'd also recently read Ladle Rat Rotten Hut - so when I pulled out Japanese stuff from my local library, I went "wait, these are phonetic systems... they're just different ways of writing sounds." So I happily started writing English sentences in the Japanese phonetic writing system.
For instance, a poem beginning:
Listen my children and you shall hear
Of the midnight ride of Paul Revere
りすてん まい ちゅづれぬ あん ゆ しゃる ひる
li-su-te-n ma-i chu-du-re-nu a-n yu sha-ru hi-ru
おぷ で みづないっと らいど おぷ ぱいる れびる
o-pu de mi-du-na-i-t-to ra-i-do o-pu pa-i-ru re-bi-ru
...and so forth.
Basically, I learned kana as an alternative phonetic system with which to write English, then switching to use the same phonetic system to write Japanese once I had it down. (I never did build up a good Japanese word vocabulary - but I can still read and write kana fluently to this day. I just don't know what the words I'm saying mean.)
Kanji, on the other hand, I never did find a good way to learn. It helps to think in terms of breaking characters down into radicals, but beyond that you just have to memorize each one, as far as I know. I did learn that studying Chinese and Japanese back-to-back is a bad idea, though; to this day, when I'm reading Chinese, sometimes the Japanese pronunciation of a word will pop out in the middle, confusing the heck out of everyone - and the reverse happens as well. I still haven't figured out a way to learn grammar, either. But that's what further explorations are for.