The Google Analytics plugin I installed recently has a bug fix update. When I logged into WordPress there was a notification about it and gave me the option to read what the update does and install it.
This update installation was very easy with a few clicks.
A new maintenance release of WordPress (3.8.1) was also available recently and installing this was also easy.
Before updating, the control panel warned to make a backup. I could have done this manually by dumping the database and copying the files with FTP, but there are many backup plugins that offer one click solutions including automated backups. I installed the WP Backupware plugin and downloaded the zip file it created. The plugin does not have a restore feature yet – hopefully it will not be necessary.