I have a Samsung Android, pretty decent, does what it needs.  

In the past I have always ran the Kindle App and bought books from Amazon.

I guess Google thought Amazon was making too much cake and they we're getting a slice, so there were changes made so that you can't buy books via the Kindle App....

The question is, those of you with Android tablets that buy e-books like I used too; Where are you buying them, what app are you using, how does that work???

*** ETA. To be more clear what I'm asking about, I've seen that now you have to log into the Amazon web page from your Smart Device (Phone or tablet), search for and buy.

Once you've done that, how do you open that book and how do you see what new books you have/have bought?

1.  You buy the book on Amazon on a web browser.  2. You open the Kindle app on your device.  Books that are in your library should show there.  You might have to go into your library in the Kindle app.

Can't help ya. I use Calibre to out my books on my Android reader

Go to the physical amazon home page on formal browser and the sign it to amazon.  Find your book and send to your kindle account.

If you bought the book via the amazon website using the same account as your kindle app the book will be in your library and you can download and read it just as you previously did. The only thing disabled is actually purchasing via the app.  Select the icon for your library and it should bring up a list of all the books you've purchased (just check that you've got "all" selected instead of "downloaded" so you can see books that aren't already stored on your tablet).

Mike

Have they got the full version of Calibre on the Android Tablet?  
I have an older Galaxy Tab A 10.1”, and while I could read using Calibre, the
library was stored on another machine on my local network.

So the browser might be the only way to read your books...

I need to send them some money. They have been consistently updating and keeping the app great.

This.

This is the way.