On this post, I will be working with Google Chrome downloading a book from Manybooks to the Kindle for PC.
This is assuming that you have chosen your book from Manybooks and are choosing the format for download. Choose .azw or .mobi for use with Kindle. Click download.

After it downloads completely, click on the file downloaded. Kindle for PC will automatically start to open.

From here you can enjoy your book!
Check out my posts on how to use the Kindle for PC here, but you probably already know :)