You don’t need a kindle device to read our e-books! They can be read on smartphones, tablets, and even on plain old computers (Windows, iOS, Linux, and ChromeOS).
The detailed instructions for downloading and registering the apps are here.
Note that you do not need to be connected to the internet when reading the downloaded books. (You do need to be connected to the internet when purchasing and downloading the books.) Also, you can purchase/download many books on to your kindle device or app. This is why, kindle devices and kindle apps are a wonderful resource when traveling.