You can edit an article either in the Front End (Public Side) or the Back End (Admin Side) of your website.  The best way is through the back end admin area.

Here's the steps:

  1. Go to the administrator backend of the website, usually http://yoursite.com/administrator
  2. Click on Content -> Articles in the upper menu
  3. Click on the name of the article and edit the article using the WYSIWYG editor
  4. When you are done click on either SAVE or SAVE AND CLOSE.
  5. Go to the website and you will see you change was made in real time.

For full Joomla documentation on editing articles click HERE.