How to write an eBook for Amazon and iPad with free sofware ?

I often see in forums, groups...  people  asking what software to use to write an eBook.
I write and edit eBooks myself so I decided to document my method which exclusively makes use of free software and allows to make ebooks for Amazon an in ePub format.
Find it here on Amazon:

• Amazon.com ($)
• Amazon.co.uk ()
• Amazon.de (€)