You can learn hiragana (ひらがな) and katakana (カタカナ) in a few days if you have some good learning materials.
After that, with some easy words to practice on, you could read basic phonetic Japanese in a few weeks if you stick with it!
Kanji (漢字) on the other hand is a life-long task, if you really go for it, say learn several kanji a week, it could still take a few years before you reach High School standard.
Even Japanese people don't know "all" kanji, they just know the basic 800-1000 or so (sometimes less) but there are thousands more technical and complex kanji that only the learned elite might know.
Because I don't study kanji at all, I only know about 200 kanji which gets me by in daily life.
I guess it all depends on why you want to learn it, do you only want to read game titles or game menus in Japanese, or do you plan on coming to live/study here?
Hope that helps!