There are a few ways to remove a book from your bookshelves on Goodreads.
If you only want to get rid of one book, you can do it from the book page. You can click on edit review or click on the edit link on the right of the bar labeled My Review. Both links go to the same edit page. Then scroll to the bottom and click on remove from my books. A pop-up window will ask if you are sure.
Another way to delete books is on the my books page. In table view, select the shelf you want to review, then find the book you no longer want on your shelves and click on the x on the far right of the screen. It will ask you if you are sure. If you are in cover view, you can only click on the edit link in the top right corner of the cover. This will give you a different version of the edit review page and instead of remove from my books, this one says delete review. Click on delete review and you’ll get a pop-up window says “You are about to remove your review”. Deleting or removing your review will remove the book from your shelves entirely, not just the review.
If you want to delete several books at one time, you can use batch edit. On the my books page, click on batch edit and it will give you little check boxes beside each book. This works in table or cover view, but only works on one page at a time, so you might want to change the number of books shown on each page before starting. You can check each book you want to delete or you can click on select all to get everything on that page. When you are ready, click on remove books on the far right, not on remove selected. Remove selected only removes the selected books from the shelf in the selector box (and only if the selected shelf is not an exclusive shelf), it doesn’t delete it from your bookshelves. This pop-up window asks, “Are you sure you want to remove these books from your collection?”