A section is the top organizational level in Joomla.  It holds categories and articles.  Categories divide sections into smaller groups. For example, this article is in the section Tutorials Database, which holds all tutorials in all categories.  This article is also in the category Joomla.  So if you only wanted to see Joomla tutorials you would navigate to the Joomla category in the Tutorials Database section.

The steps for adding a Section and adding a Category are very similar:

1) If you are on the Welcome page (the page you are sent to after logging in), you can click the large "Section Manager" or "Category Manager" button:

If you are in any other area of Joomla, you can hover your cursor over the word "Content" in the top left corner.  Other options will appear when you do this.

*Note:   The other options will only appear if you are not in edit mode, which is denoted with the word [Edit] next to the title of the page you're on.  Example: "Article:  [Edit]" or "User:  [Edit]"

Click either "Section Manager" or "Category Manager."

2) Click the "New" button.

3) You can now add content to the new section or new category page.

or

4) When you are done adding content, click the "Save" button.  This will save your changes and exit the article editor. 

If you would like to save without exiting the article, you can click "Apply."  Then click "Save" when you are ready to exit the article editor.