I download from the library directly to my iPad using the Overdrive Media Console app. At first I had problems because everything I tried to download had a wait list, though it didn't tell me that. So if I put in on a wish list, and it's available, I get the option to add to my cart, then the option to check out, then option to download. Otherwise, it says on my wish list.
Using the Nook App to get books from B&N, I finally figured out the nuances there. First put it in my virtual cart, then pay (even free books get a $0.00 charged to credit card). Then wait for an email from B&N that it's available for download. That might be minutes later, but once it wasn't until the next day. Then download which, by the way, is slow.
Downloading from Amazon to iPad using Kindle app is smooth and fast.
Oh, interesting. It looks like (just from what I'm reading on line) that the Sony doesn't have internet access, either Wi-fi or cell. It looks like the only way you can get books is to download them to your PC/ Mac then transfer them to your Sony reader. Which, as long as you have your computer handy, is hardly a big deal. It would only be a problem traveling.