When writing a sentence, Do you write, "So and so said...", or "So and So stated...." ?
I always thought when using "said", you are paraphrasing someone's comment, and using "stated", you write someone's exact words.
Technically, neither. I would use "says" or "states."
In formal academic writing (arts & sciences), you will say "says" (informal) or "states" (formal), or you may interchange the two if your discourse relies heavily on testimony. Regardless, keep it simple and understated: the focus should not be on the lead-in sentence or the tag, but on the quote or paraphrase itself.
The reason it should be present tense is that the language of academia must be current and up-to-date. Also, present tense suggests not only the past, but it connotes the future as well (that the idea is still relevant). Even if you are discussing a novel written in 1960 about the 1930s, as The Autobiography of Malcolm X is, you will want to say, "Malcolm X says that the race problem in America is thus and so...".
I don't believe there is any technical difference between said and stated. Stated is probably a little more formal, but that's all. The quotation marks, or lack thereof, determine whether the quote is paraphrased or cited exactly. So use said when you want to be informal, and stated when you want to be formal.
Interestingly, what I've read suggests that attributions are largely irrelevant anyway. Readers tend to pass right over them to get to the name the quote is attributed to, and don't actually read the attribution. This takes a little pressure off of writers, since we don't have to spend too much time worrying about varying our attributions. At least that's the theory.
That's a pretty good rule of thumb. "Someone stated" is generally considered more formal and appropriate for term papers, research papers, speeches and presentations. "Someone said" is more informal, good for conversation, prose style writing, and journal writing. It's also considered proper to use "stated" when citing someone else's formal research or argument from a paper or article, or when the person quoted is an academic or a leader.
Anytime you are looking to persuade someone of a thesis or case, it is generally better to use the formal expression whenever possible. "According to" also works as formal in this case.