If you are using the 3rd Party Extension JCE Editor with your Joomla 3 installation, you can easily select from existing styles set up in your CSS stylesheets. You use the Styles pulldown selector in the JCE Editor to select the class that you want to apply to the selected element. By linking your stylesheet(s) to JCE Editor it makes these styles available in the dashboard and also for the Advanced tab in the Image Manager.

To link to your stylesheet follow these steps:

Components -> JCE Editor -> Editor Global Configuration -> Formatting & Display -> Editor Styles

 Use the pulldown selector and choose Custom CSS Files. A text box will appear below where you enter the path to your CSS stylesheet.

Select Save and the next time you are in the JCE Text editor and you want to apply a class to something like a <p> tag or any other tag that allows classes, you can simply highlight the selection and use the pulldown selector to add you desired class.  

What it does to the HTML in the background is add class="mystyle" inside the opening tag, where mystle represents your selected style.editor-styles