Your learning method is of course going to depend on who you are as a learner. Ryoko mentioned that Japanese begin learning at a young age, and I would like to point out that adults can probably learn more efficiently than children, through various strategies.
Just to give you an idea, the kyouiku kanji is a list of 1,006 kanji in 6 years. I learned more than the 2,136 jouyou in just about 5. I think most university Japanese courses would have you at over 1,000 in 4. But, that is reading them, not writing. I can't write all 2,000 some from memory, but considering the use of computers in everyday life writing them isn't really all that necessary.
Working on my last set of kanji, I made a schedule to learn the meaning of 5 new kanji a day. That's quite a bit but even if you did something like 2 a day, or 5 every week day with breaks on the weekend, you're still going quickly. Some people will argue that you'll want to study the readings of the kanji like that as well, but most people think it's best to learn the kanji in the context of learning new words. They don't really learn kanji separately at all. I only do the meaning separately from the words, so that if I see a compound word I haven't learned, I can probably still understand it.
Anyway, as I said earlier, methods really vary depending on the person. It's best to find a method and schedule that works for you that you feel comfortable sticking to.