Edit: I originally advised to download an .epub file. It’s actually a .mobi file. Sorry about the confusion.
Someone asked me to put together instructions on this. Since I did it for them, I thought I may as well publish it here.
1. Go to http://www.gutenberg.org
2. Search for books by author, title, or subject.
3. Select your book.
4. Click on an MOBI format to download.
5. Go to your “downloads” file.
6. Find your book. It will be named something like “pg-86.mobi” or “pg-86withimages.mobi”. You may want to re-name it so you’ll know which book it is later.
7. Go to Amazon, and under “Your Account” go to “Manage Your Content and Devices”.
8. Once there, go to “Settings”.
9. At the bottom, under “Personal Document Settings”, you will see the email address for your Kindle account.
10. Go to your regular email program, and attach the .epub file to a new email, and send to your Kindle account. Your new ebook should show up on your Kindle pretty quickly.
NOTE: Amazon FAQ says that there is a limit to the number of free books / outside material you may upload, though it doesn’t specify what that limit is.