There has been some disagreement in my other online searches, and in my own education.
Assuming that I do not know if the individual addressed is married, when should I use Miss Brown, and when should I use Ms. Brown?
According to The American Heritage Book of English Usage,
Using Ms. obviates the need for the guesswork involved in figuring out whether to address someone as Mrs. or Miss: you can’t go wrong with Ms. Whether the woman you are addressing is married or unmarried, has changed her name or not, Ms. is always correct. And the beauty of Ms. is that this information becomes irrelevant, as it should be — and as it has always been for men.
RegDwight has given a correct modern answer. The traditional approach would be different. Adopting this approach will sound like you're living in the 1950s or earlier, so you shouldn't actually do this, but I thought it would be useful to document what the modern system is reacting against.
This was the usual approach before 1960 or so (after the separation of Mrs. and Miss from the original Mistress in the seventeenth century). The use of Ms. (at all) was controversial from its proposal by Sheila Michaels in 1961 until some point in the 1980s - William Safire's use of it for Geraldine Ferraro in 1984 is often seen as the pivotal moment for acceptance by its former opponents, in that someone as traditionalist as Safire realised that he couldn't use anything else.
I believe that the announcement of the engagement of "Prince Henry of Wales and Ms. Meghan Markle" on 27 November 2017 is the definitive proof that the title is appropriate in the highest of society.
If you're writing historical fiction, or you want a character to sound very old-fashioned, then using the traditional forms would be appropriate; even if not, it's useful to know what they were.
(This question has been referenced from another marked as a duplicate, so I'm adding an answer here even though this question is old.)
The catch is that this is all politically/socially charged.
The title "Ms" was invented in the 70s (or at least that's when it became widely known) by feminists who objected to being "identified based purely on their relationship with men", to use a phrase that was commonly repeated at the time. Their intent was that Miss and Mrs should be abolished and replaced with this new "non-sexist" term. But because the term was advanced as part of a specific philosophy or social agenda, women who did not support that agenda objected to having the term applied to them. So what we really ended up with was that feminist women identified themselves as "Ms", unmarried non-feminist women identified themselves as "Miss", and married non-feminist women identified themselves as "Mrs".
What could under other circumstances have simplified titles, reducing 2 to 1, resulted instead in complicating them, increasing 2 to 3.
I don't think there's as much heat attached to it today as there was back then. But you can't just say, "Oh, it's easier to use Ms for all women because then I don't have to know whether or not they're married." Many non-feminist women don't like the title and object to having it applied to them, just as many feminist women object to the titles Miss and Mrs.
The only "easy answer" is to call a woman by the title she prefers. If she refers to herself as "Mrs Mary Smith", then that's what you should call her. If you don't have anything from her giving a title, ask her.
Well, I suppose if you want to make a social point, for or against feminism, you could use the title you prefer whether she likes it or not.
Personally, I just avoid using any title at all when I can. I just refer to her as "Mary Smith" without any Miss, Mrs, or Ms.
A rather strange point was raised in the accepted answer to this question. Personally, I wish this information were relevant for both men and women, but the fact is, it is a feature of our language that men are always styled 'Mr' unless they have some other title or style, and women have the privilege of being styled 'Miss' or 'Mrs'. Some women will be seriously offended if you don't address them by their preferred title. In business correspondence, 'Ms' is almost always appropriate, but in social correspondence, one would do well to try to find out what the lady in question prefers.