If you are studying Japanese through studying anime alone you are soon to find out that there is a large problem: the inability to comprehend or reproduce the written Japanese language. Although studying through anime is a great resource through verbal comprehension and pronunciation it does nothing to supplement reading and writing.
As I'm sure you know (since you are reading this blog) there are 4 written languages in the Japanese Language. The first is Hiragana (ひらがな), this is the basic writing method used when Kanji is not written / available for the word written. This alphabet is phonetic meaning that each characater represents a sound (i.e は=ha つ = tsu).
The second is Katakana (カタカナ), this is the writing system used to spell out foreign words, used to emphasize (the equivalent of writing in all caps or underlined etc.), or used to product names or things you want to stand out. This alphabet is also phonetic.
The third is Kanji(漢字). This is the alphabet that uses Chinese characters. This alphabet is the hard one to learn, there are about 2000 kanji necessary to comprehend this writing. Each character has 2 readings, a Chinese reading and a Japanese reading, the characters themselves also have a pictographical meaning as well. There are also compound Kanji that are pretty much the equivalent of the English compound words.
It is possible and very easy to learn Hiragana and Katakana in 3 or so days. I would suggest doing this as soon as possible as it gives instant gratification to be able to read atleast some words in the Japanese language. Kanji on the other time is going to take some time....a lot of time. The best method I've found to learning Kanji is to use a book called "Remembering the Kanji" by James Heisig. If you look hard enough it is easy to find this in a .PDF document....
The book uses Mnemonics to remember the 2000 or so Kanji you are going to need to learn.
I highly suggest learning the written Japanese language in addition to learning the verbal language from Anime. You can get a lot out of Kanji, mainly word comprehension wise. Also, let's face it. If you can understand words but not read them then you have no more control over the language than a 4 year old.