Direct answer
The best way to save web fiction for an e-reader is to export a clean EPUB with a sensible title, author name, chapter order, and optional cover image. That gives the reading app or device the metadata it needs for a stable library entry.
Why EPUB is the right default
EPUB is easier to transfer and catalog than a pile of open browser tabs or copied documents. It keeps the chapter order intact and works across most reading apps and e-readers.
Next step after export
Once the file is ready, follow the EPUB to e-reader guide or the Send EPUB to Kindle guide.