You have a choice of purchasing either the “epub” or “mobi” formatted versions of the book. Most eBook readers handle epub format easily. Amazon’s Kindle works very well with the “mobi” formated version, so if you use a Kindle, you might as well purchase that version.
On Android phones, there are many eBook reader Apps. Both Nook, Kobo and Kindle Apps are free and work reasonably well, though they do want you to create accounts and they will try to sell you more stuff. There are other apps that can be used to read eBooks, with FBReader being free and recommended by a number of sites.
It is quite similar with iPhones, with Nook, Kobo, and Kindle Apps being available. Apple also has a eBook reader app as well.
The easiest way to get the file to your phone or pad device is to open the purchase email you have received and download the book to your device.
On Windows it is a little more frustrating to use Kobo, or Kindle. It is not clear how you access the file through their apps. The Windows 10 version of Kobo works fine (import icon at bottom right of your library page), but it is not obvious how you import files with Kobo Desktop.
There are a lot of free eReaders available for Windows, with the free Icecream eBook reader being highly recommended: http://icecreamapps.com/Ebook-Reader/
For Apple we have heard that the Apples own iBooks works well with ePub and that Kitabu is free and is also good.