Hi, I'm about 800 kanji into using the Heisig method. I'm not very good at explaining things, but I'll give it a shot.
Heisig's method is typically made to be used in tandem with his book,
Remembering the Kanji. It breaks down the radicals (or elements, as he calls them) in kanji and associates each of those radicals with a meaning, which you can then use to make stories about kanji. The purpose of the method is to gain the ability to recognize and write kanji (with proper stroke order) without having to do any brute force learning, such as writing them hundreds of times until you can see them in your sleep.
It works beautifully together with an SRS (spaced repetition software) like
Anki, or the
Leitner system-based website
Reviewing the Kanji, which specializes in the Heisig method of kanji learning.
An example from the RevtK website, of the 779th kanji in the book:
[銃] is a kanji associated with "guns." It's composed of the elements [金] "gold/metal" and [充], "allot."
The story someone used was:
What is a gun but a device for allotting pieces of metal? One for you - BANG!...One for you - BANG!...One for you - BANG!...One for you - BANG!...etc. Common criticisms are that he doesn't teach the kanji in the
jouyou list order, which is how schoolchildren in Japan learn them, or in order of how frequently they're seen, but instead they're organized by both simplicity and their elements. That can mean that it won't be until you've learned 901 other kanji that you finally get to do #902, [私] (わたし), which is "I." The other issue people have is that the method doesn't teach you the readings of the kanji, only how to recognize them. So when you finish the book, and you see a sentence like "子猫ちゃんはもう眠っているね", you won't know how to read the kanji parts out loud, but you'll be able to see that they mean "Child-kitten" and "sleep." Once you learn kana and basic grammar, the meaning sentence falls into place with ease. It doesn't always work out that way, especially with complicated kanji compounds, though.
So, the method is more like a big, whopping stepping stone toward kanji literacy than it is a total solution for learning everything you need to know about them.
To answer the "how to do it" part, go out and buy
the book and get an account (they're free) at
RevtK. The site has an info section that explains the rest from there.
But personally, I can't recommend it (together with the Reviewing the Kanji website) enough. I tried learning kanji by writing them out, flashcards, and even a site called Kanjidicks, which basically mentally scarred you into remembering them, but nothing worked as well for my poor memory as Heisig's method has. Even if I might have to use flashcards to memorize the readings later, I can at least recognize each individual kanji and their basic definitions now, opposed to every single card looking like someone sneezed on it while holding a calligraphy brush.
Sorry this is a pretty wordy answer. You can find more info on the method/books in the Remembering the Kanji book reviews on Amazon.com, on the
Reviewing the Kanji forums, or just by Googling it. It's a pretty popular method, so there are quite a few reviews out there.