This came up in a group I’m in on FB so I thought I’d just write a quick blog post with screenshots for anyone who needs it. This is for authors who want to update their cover on Goodreads and have it be the cover that shows by default.
First, I’m going to assume that you’ve already set yourself up as an author on Goodreads. If you haven’t you need to submit to them to be listed as an author and go through some sort of process where I think you give them a link to your website.
Once you’re set up as an author, when you log in you should have access to the Author Dashboard. It’s under the dropdown on the right-hand side that usually has your author photo. (I don’t have a photo on my account so it’s just a little circle with a person reading a book for me.)

Click on Author Dashboard. That’s going to take you to a stats page that shows all your books:

If you ever want to manually add one of your books, this is where you can do that. Click on the small “Add A Book” option above the title listing. (I have to do this with every M.L. Humphrey release because there’s another M.L. Humphrey on Goodreads and titles default to that author’s profile instead of mine unless I add them first. My listing actually has two spaces between the L and the Humphrey part of the name since I was the second M.L. Humphrey to be listed on Goodreads.)
If what you want to do instead is update a cover, click on that book’s name to bring up the book page:

Down by the Other Editions section there should be an option to “Add An Alternate Cover Edition”. Click on that.
This will result in a pop up that tells you the identifier information is going to move to the new version. Click OK.

If you get an error message about it not being able to create a new version then click on the other existing thumbnails for that book until you find the one that has the ASIN/ISBN currently assigned to it and try again. (I’ve only run into this once.)
Once you say OK, that should bring up the Edit Book page for that title. On the right-hand side there’s a place to upload the new cover. Click on Browse, find your cover, click on it, and then click on Upload Photo.

You should now see a thumbnail of the updated cover on the right-hand side. Click on “Set This Book As The Primary Edition For This Work” to make that the cover that will show for all users.
Scroll to the bottom and Save Changes.
And that should be it. If you exit Goodreads and just go to the main page and do a search for your book it should come up with your updated book cover as the image.