This tutorial is ONLY for those using the UpDraftplus Backups plugin to backup your database and files. As of WordPress 3.7 all maintenance releases (x.x.1, x.x.2, etc.) are upgraded automatically. You will only need to do your backups for major releases (3.8, 3.9, 4.0, etc).
Navigate to Settings > UpdraftPlus Backups in your WordPress dashboard sidebar.
Click the Backup Now button and allow the backups to process. Once done check your email for the backup emails or the backup log report. If you receive your backups by email then there should be one for themes, one for uploads, one for plugins, and one for the database. Depending on your site you may have additional folders that get backed up as well and an email for each. If your backups are stored on your server then you will only receive a log report.
After you’ve checked your email and made sure you have your backups then you can safely use the WordPress one-click update feature. Navigate to your main Dashboard page by clicking Dashboard in the sidebar. Then click on the “Please Update Now” link at the top.
Click the Update Now button. WordPress will download and upgrade automatically. Once done it will redirect to the Dashboard Home page and list the newest features available to you.
Detailed instructions in the screenshots below: