A class can be used several times, while an ID can only be used once, so you should use classes for items that you know you're going to use a lot. An example would be if you wanted to give all the paragraphs on your webpage the same styling, you would use classes.
Standards specify that any given ID name can only be referenced once within a page or document. Use IDs when there is only one occurence per page. Use classes when there are one or more occurences per page.