Well, I did this guide because I was (following this tutorial to) transferring e-books I originally download for my iPad(which I sold away a long time ago, the iBooks app I used uses EPUB by default) to a newly-acquired Kindle Paperwhite(the 2012 version because the store didn't have the newer one. was a gift) and when the "calibre" app I used downloaded a description that mentioned a digital edition, I decided to just download from the Kindle store directly instead of sideloading the converted EPUB.
Now I do warn you that this will not give you the "(book name)_(AZN number).sdr" folder. That means no "X-Ray" support.
*I stayed at a holiday apartment in Gold Coast(in Australia) that was like that, connecting through their ADSL(I think) connection with an Acer laptop that was the exact same one featured in my "Turn a laptop into a desktop" Instructable, I fixed the fan on it but it kept falling apart and later, I gave up and sold it for parts, bought another tablet PC, which slowly led up to my surface pro that I have today,
Step 1: Downloading E-books
Assuming you already have the Amazon pages for the books you want already open, go ahead and download them. Change the "deliver to" to "transfer via computer" and click the buy now button like normal.
You need to select your Kindle device so that Amazon can send the correct version of AZW format for the file, as there is AZW, AZW2 and AZW3 as far as I know. I selected "KBookworm", a 2012 Paperwhite.
Save your e-book and repeat this step with the other e-books you want to purchase.
Step 2: Copy to Device
(The desktop wallpaper can be downloaded from here)
Step 3: Enjoy!
You're done. But here's a bonus.
Kindle Touch/Paperwhite screenshots: (Thanks to this guide!) Tap the top left and bottom right, or the top right and bottom left of the screen at the same time. The screen should flash, Find the screenshot as well as a "wininfo" file in the root of your device. Tested working on Paperwhite, not sure about Touch.