To the left of each book by default is an empty checkbox. When you click that, it by default marks it as “read”. It also pops up the book manage screen like below:

If all you want to do is mark a book read, you can close this popup. However this also gives you the option to:
– Change the status from “Read” to “Did Not Finish”, “Want To Read”, or “Not Interested”.
– Reset the status of the book to unread by clicking “None”.
– Make any private notes about the book that are only viewable to you.
– Change the date you read the book.
– Give a rating of the book.
– Write a review of the book, which will be shown on the books page.
You can also disable this popup in your settings. What this means is that when you click on a checkbox, a checkmark will appear and the book will be marked as read. Then if you want to do anything else, you can click on the checkmarked checkbox to make the book manage popup appear.