To publish your course (or parts of your course), click on the Publish button and select the modules you'd like to publish from the list, then click on the Publish changes button. Changes will be published immediately. You can also revert back to to the last published version, by clicking on the Revert button instead.
How do I know if there are changes to be published?
When creating a course, you'll notice the Publish button on the top right corner of your screen.
Everytime you make a change to your course, you will see the yellow number on the button go up (it counts the number of unpublished changes).
You can also see the screens that have unpublished changes from the navigation menu on the left side (identified with a yellow dot)
When you publish your changes, the yellow number on the Publish button will disappear, and so will the yellow dots in the navigation menu.