You use .class when you have something like this:
You would use .class to select that using CSS. For #id's you would select those by using:
A div is used to collectively wrap around several elements where needed. Good examples are sidebars, wrappers, and sometimes footers. Don't overuse them though. As for spans, you should really only use those when you have to style text inside a p tag (or other tag) differently than the rest of the text in that tag.