If before the quote the word "saying" or "said" is used, does a comma always have to be used before it? When does a comma not have to be used?
I don't believe there is any special rule governing how to punctuate before a quotation (assuming this isn't dialogue in fiction, which is when use of the word "said," or substitutes for it, generally requires special treatment). I punctuate a sentence containing a short quote in the same way I would any other. Typically, if the quotation is a complete sentence (i.e., subject + predicate), I would separate it from the introductory clause using either a colon or a comma, depending on what feels right in the situation.
I think in this example, either one works, but I like the comma best because of the informal feel of the sentence (at least it sounds informal in isolation from its context) and the short length of the quotation. If this were an academic paper, and the quotation longer or more substantial, I would probably opt for a colon so as to call special attention to it.
I am not 100% sure if there is some strange rule in English for this... but rather than a comma I would use a colon.
The OED says:
A quotation fits the first definition much better than the second in my opinion.