The difference is easier than you might imagine. You should use single quotation marks (') or doubles (") as you wish, but you should be consistent throughout your document. If you decide to use doubles, then you should only use singles when quotation marks are required within a quotation. For example:
My mum said: "..and then Gene said, 'you must be joking' before she stormed out."
Can you see? The singles are used within the doubles. You can use singles througout your document and only use doubles when you require quotation marks within a quoation.
Therefore, it should be quite rare to see both singles and doubles in the same document.