There are two ways to get stories from the site onto an Amazon Kindle:

#1

When you browse the site on the kindle directly, you should get the small screen version of the site which has a 'Download' button. (If you don't see the small screen version of the site and get the full version, then click the 'Settings' link in any listings page, and from the screen size menu, choose 'small' instead of auto or normal.) Clicking the 'Download' button will reveal a kindle button. Click the kindle button to download the story to the kindle.

Method #1 is fairly straight forward. However, the kindle's controls aren't that intuitive for browsing site. Second, the file that the site sends to the kindle directly doesn't contain any formatting and no table of contents.

Method #2 is more involved, but it results in better files on the kindle:

#2:

Browse the site using your PC. You need to download the EPUB versions of the files and then use 'Calibre' to open the EPUB files and send them to the kindle.

Calibre is free and you can get it here:

http://calibre-ebook.com/download

If you don't want to use calibre, then you can download the PDB files, then change the filename extension from .pdb to .prc and copy them to the kindle.