Custom walkers seem to be a poorly-documented area of WP. Online tutorials focus on styling the output, not on directing the walker to go where you want it.
I am reading the code, but I wonder if there’s a good resource I’m missing. If you know about walkers, how and where did you learn about them?
I stumbled across this article, I think it could be of tremendous use to you. It helped me understand it a lot better.
I believe there was a question on here in which (I think) @Rarst answered that linked to it, but I can’t seem to find it. If someone can find it and edit my answer in place of this that would be great!
EDIT: Found another pretty good resource you can find here.
EDIT: More excellent resources below you can look through. I made the ones that are extremely useful in my opinion bold!
http://resources.mdbitz.com/2010/08/creating-a-wordpress-custom-page-walker
This one in my opinion is the best explanation to modifying the output of the items. It actually also explains what each of the Walker Class functions do.
http://wpti.ps/functions/extending-wordpress-walker-class/
This one was a result of the first link, as you can see they link to the first article in this article. 🙂
http://www.jeangalea.com/wordpress/how-to-use-wordpress-walker-classes
This has some that I posted above as well as like 5-6 other articles on extending the Walker Class.