I hope you enjoy RTK! There are tons of discussions about this topic, so I highly recommend you browse/search the forums here. Also, read the introduction in the book, that should clear up some of your questions. I'll try to summarize the method and what I do:
Here's an overview of the method:
-Learn the simplest characters (or pieces of characters) first, then build other characters using characters you already know.
-Each character is associated with an English keyword, which is normally tied to the basic meaning.
-You make stories with the keywords to remember how to write the characters. These stories are supposed to be visual, but I often just rely on a sentence with the keywords to remember the character. Seems to work just as well :-). Maybe I'm visualizing it and not realizing it too.
-It's good to review characters you have studied with a spaced-reptition flashcard program, such as Anki (it's free and works on Windows, Mac, Linux). People have already made flaschards for the book and shared them, so you can download a deck and start using it immediately. (Link:
http://ankisrs.net/). Or you can use this website's flashcards.
-The first section of the book gives you stories, but the last part doesn't and expects you to make your own. You can look through the stories shared here and choose one that works best for you. Sometimes I don't like Heisig's stories so I use the ones from this website instead even when he gives one.
-This book separates the sound from the writing/meaning, but people have had success adding one of the sounds into their stories as a keyword, so you could go that route (or search on the Movie Method or Kanji Town in the forums, which are other methods).
The more you practice the characters and see them in context, the less you rely on the story to remember them. Eventually the story and the keyword disappear and you just know the character. It's much more fun than writing the characters over and over and over again!
You shouldn't need to write them repeatedly in order to remember how to write them. I generally only write a character a maximum of three times when I first learn it. The whole point of RTK is to limit the amount of repetitive/boring memorization of writing that you would do with other methods.
Some people take a very long time to visualize their stories. I find that I tend to just think of a sentence that relates the keywords together and that I think I'll remember easily. Sometimes my stories are very visual in my mind, other times they aren't. Learning 10-20 kanji should take you less than an hour, even if you create your own stories. I use the stories from this website, so I can easily "learn" 10 kanji in 20 minutes or less.
This is what I normally do every day:
For each character:
1) Look at the character in the book.
2) Read the story from the book, or get one from another website, or make my own.
3) Practice writing the character once or twice while repeating the story in my head (make sure your stroke order is correct).
I try to do 10 per day (this takes me only 10 to 20 minutes since I normally don't make my own stories). After I've practiced 10, I review them in Anki later that day as flashcards.
I also review older flashcards each day. The flashcards have the keyword on the front and the character as the answer to make sure you know how to write it properly. When I review:
1) Look at the keyword.
2) Remember the story
3) Write the character.
4) Check answer and grade yourself.
If I got it wrong, I look at the story again and write it a couple of times. I basically treat it as a new character.
It's reviewing the flashcards that takes the most time, as it builds up the more you learn. 10 per day makes it manageable. It's important to review the cards regularly though, otherwise you will forget and the number of cards to review becomes huge.
You can't expect to get 100% correct each day. If you get 100% correct, that's great, but the whole purpose of spaced-repetition is that if you get it wrong, you'll see the card again the next day. So if you keep failing a character, you'll learn it eventually because you'll see it more often than other cards. Getting around 75% correct and above is good. The important thing is to keep moving forward and not worry about perfection.
Good luck!