There are a few different ways to do this. You may want to skip to the section that applies to you.
You Have a Kindle
If you have an actual Kindle device, in my opinion, the easiest way is simply to email the book to your Kindle. Every Kindle has its own email address. The trouble is, to avoid spam, Kindles automatically block all incoming emails, unless they are from an “approved” sender. Here’s how to find your Kindle’s email address and tell it to accept email from you.
You Don’t Have a Kindle, but You Have the Kindle App on Your Computer, Tablet, or Phone
If you’re checking your email on a computer that has the Kindle app installed, simply download the mobi file in the attachment. Then, go to your downloads folder or wherever you saved it and double-click the file. It should automatically open up in the Kindle app, and you’ll be able to start reading immediately.
If you have the Kindle app on another device, follow the 8 steps above to send the book to your Kindle’s email address.
Note: Those 8 steps work for most devices, but not all. Here’s what Amazon has to say about it:
In that case, you’ll probably see a screen like the one below, that skips the section above “Personal Document Settings” where the Kindle’s address would normally be:
In that case, I suggest you install the Kindle app on your computer (see the instructions below) or ask the author if he/she could possibly send you a PDF instead.
You Don’t Have a Kindle or the Kindle App Installed on Any Device
It’s easy (and free!) to install the Kindle app. Just go to this link.
Then click on whichever of the black buttons applies to your device. Follow the instructions to download and install it. Once you’ve done that, come back here and follow the instructions in the section above (“You Don’t Have a Kindle, but …”)