If you bought the book file using your iPad, start at stage 1 in these instructions.

If you bought and saved the book file using a computer, email it to your iPad.
When you open the email it should automatically download and you will already be at stage 6 (of 8).

The first set of instructions are for .epub files using Apple's Books App that comes pre-installed with iPads using iPadOS. This is the icon for Books (formerly called iBooks), both use this icon.

Older iPads (iOS 12 and earlier) have a much easier and more obvious way of doing all this.

If you want to install the .mobi file, using the Kindle App, see the second set of instructions below.

These screenshots are from my own iPad. Follow the red instructions I have written on them.

1. When you click the link to download the book, you will see this.

2. As soon as the connection is established, you will see this.

3. When the book has downloaded, you will see this.

4. After you have tapped it, you will see this.

You can also get to the Downloads folder using the Files App.

5. When you have tapped the file, you will see this.

6. When you have tapped the button, you will see this.

7. When you slide the icons left, you will see this.

8. When you tap Open in Books, the book will open in Books, ready to read.

This is what it looks like in my Books App Library.
You can also use this method with other suitable Apps by repeating steps 3, 4, 5, & 6 and choosing a different destination at step 7.

For .mobi files

1. When you click the link to download the book, you will see this.

2. As soon as the connection is established, you will see this.

3. When the book has downloaded, you will see this.

4. After you have tapped it, you will see this.

You can also get to the Downloads folder using the Files App.

5. When you have tapped the file, you will see this.

6. When you have tapped the button, you will see this.

7. (1) When you have tapped the button, you will see this.

7. (2) When you have tapped the button, you will see this.

8. In either case, when you have tapped the send button, you will see this.

Usually, it does not take much time to appear, certainly not enough to make a cup of tea, but it is dependant on the size of the book, the speed of your internet connection and how busy Amazon's servers are.

9. This is what it looks like in my Kindle App Library. Click the book to start reading.