So you have downloaded an ebook (probably in ePub format), and want to get it onto your Kindle device.
The easiest way to do it is using the Kindle Personal Document Service:
1. Convert your eBook file
The Kindle service can't handle an ePub file, only .mobi (but see the end of this article for other document formats supported). You will need to convert it to .mobi format. Here is an online converter that will do it for free http://ebook.online-convert.com/convert-to-mobi
[There may be some formatting issues with the conversion process, but I have not encountered any significant issues with text based books].
2. Find your Kindle email address
You should add one of these to your email address book so you can find it easily next time.
3. Email the file as an attachment to your Kindle account.
Just a blank email will be fine with the file attached to it.
Wait a few minutes for Amazon to process the file and add it to your library.
4. Turn on your Kindle device and look for the file.
Important: The file will be listed under documents rather than books so you need to look in the documents section.
You may need to re-synchronize or let the file download over wifi.
If it has not downloaded it may be listed under "Cloud" and you will have to click on it to download it to your device.
Here is the current list of supported file formats from Amazon.
The Kindle Personal Document Service can convert and deliver the following types of documents:
Microsoft Word (.doc, .docx)
Rich Text Format (.rtf)
HTML (.htm, .html)
Text (.txt) documents
Archived documents (zip , x-zip) and compressed archived documents
Moving ebooks from the document to book sections on the Kindle
Why does your book end up in the Documents section? This is because the Kindle Personal Document Service adds a "PDOC" tag to the file when it converts it. I believe that its possible to transfer the files using a cable and some additional software to avoid this. but unless you are doing a lot of it its not worth the complexity.