Another big reason for using CSS rather than inline styles on pages is because it saves a lot of time - if your realize after the fact that you want to change the style of an element which repeats throughout the site, CSS allows you to make the change once and have it instantly globally changed while inline styling would require modification in every place that element occurs.
With HTML5 the following is now the correct method of linking to a stylesheet: <link rel="stylesheet" href="styles.css">
Class selectors don't necessarily have to start with the element. For example .my-div-class a should work just as well as div.my-div-class