What education does one need to be called "Professor" in the United States of America? A woman with a law degree in a junior college paralegal program insists on being called professor at a local community college. She is the only one in the whole school that does this. Is this normal?
I completely agree with the answers by ff524 and Pete L. Clark, but I'd like to highlight one issue that's in the background here, regarding whether this behavior is normal. When someone makes a point of emphasizing a professional title, it might be because they are pompous, but they might actually have a good reason for it. It's difficult to do your job well if the people you are interacting with don't maintain an adequate level of respect and professionalism, and insisting on titles can be an effective way to control the tone of your interactions.
Whether this is helpful is often correlated with gender or race: many white men are treated respectfully by default, while women or minorities sometimes find that students or colleagues interact with them in troubling ways that don't arise nearly as often for their white male coworkers. For example, students sometimes expect unreasonably forgiving and nurturing behavior from women and react harshly if they don't get it, students sometimes disrespect women in class and try to challenge or undermine their authority (for no intellectually compelling reason), etc. Of course this doesn't always happen, but it's a real problem for some people.
Insisting on the use of a formal title is one way to address this issue. You run the risk of looking pompous or uppity, but you are willing to take that risk in exchange for reminding everyone of your position and your desire to maintain a formal and respectful tone. This may not be the best solution in any given circumstances, but it works well enough that it's reasonably common.
So my recommendation is to approach this issue with some charity. If you hear complaints about someone insisting on a title that nobody else cares as much about, especially a woman or minority, you should keep in mind that it may be their way of dealing with a difficult situation.
I'll answer the general question in the title of your post:
What education does one need to be called “Professor” in the United States of America?
None at all. In the United States, someone who holds an appointment as a professor (of any rank, including professor-like positions that may not even include "professor" in their official name) at a university may be addressed as "Professor." It is not a matter of their level of education, but of their job title.
A woman with a law degree in a junior college paralegal program insists on being called professor at a local community college. She is the only one in the whole school that does this. Is this normal?
If she has an appointment that is in the range of "professor" positions, then she is perfectly entitled to insist on being addressed as "professor."
No specific educational background is necessary to be called "Professor" in the United States. It is not an honorific like "Dr." which refers to a specific degree. (There have been some famous academics who had no more than a BA, e.g. Lyman Kittredge. This is less common as time goes on, but there are certainly many professors without terminal degrees in their field.) "Professor" is a formal job title in the field of higher education, and if someone holds that title at their institution then they can use it with legitimacy.
In general, anyone can "insist" upon being called anything, and the other party can then decide how they want to respond. I could refuse to call my physician "Dr." if I chose to; what happens then is up to them. Insisting on being called by your job title while on the job seems reasonable to me.
"Is this normal?" can be a hard question to answer for strangers on the internet. Granting the premise that she is the only faculty member at the institution that wants to be called "Professor", then...it seems to follow that it's not normal at that institution. But there are many other American professors who want to be called "Professor" and many institutions where this is the most common appellation, so in that sense the practice is normal.
(Added: @AnonymousMathematician gives some compelling conditions in which it may be appropriate to be the only faculty member at their institution who insists on this.)
Sharing my own story since it comes in the grey area and might be helpful to some.
I recently completed a Master's degree in Computer Science and was asked to teach an undergraduate class the next semester. The version of this question I asked my wife was, "what should I have the students call me?" She was merely amused and responded why would it matter but astutely mentioned that it should be enough for the students to know the university was satisfied with my credentials and thus allow me to teach there. In the same vein of other answers here, I'm not insisting on formality for its own sake but am trying to juggle lots of cultural norms involving titles in an educational setting and so forth.
Since I neither have a PhD nor do I have a medical degree, I shouldn't expect to be called doctor; the question is whether to correct a student who addresses me that way. It hasn't happened but I've resolved to correct them if it does, that just leaves me with what to ask them to use in place of 'Dr.' The natural choices are the forms Prof. French or Mr. French. During my undergrad days when we had an instructor that did not have a PhD. we would make sure to use Mr. or Mrs. (in those days the Ms./Mrs. debate had not flared up yet).
In my case the question came down to whether I could be referred to as Prof. French without either confusing a student who then expected I held a PhD or somehow being seen as borrowing the title as a form of ego-stroking. There are several questions that dance around the issue like, is it ok to call Prof. X Mr. X or addressing a friend who teaches after joining his lab or at what point can I refer to my professor by their first name
What cleared it up for me was my appointment letter, which stated unambiguously that I was being appointed as an adjunct professor. At the beginning of class I wrote my full name on the board but did not include my work history or my degrees, heeding my wife's advice on not feeling the need to express my credentials to the students as I don't need to prove anything to them. When students address me they use Professor French both in person and in emails and that works for me.
My oldest daughter has recently finished not only a degree in teaching - and has been teaching in a primary school for years -but completed a master's of her own, but a different field, the same semester as I completed mine. I consulted with her about teaching in general and she had a ton of good information on how to manage a classroom. We agreed that in my case I didn't want to tell them it was my first time teaching; mainly because while it might make me feel less of a need to apologize for mistakes or oversights it would give the students a seed of doubt, however tiny, which might serve as a distraction.
As it turns out, the teaching assistant for the class is a PhD student so she addresses me in emails as Mr. French which I prefer because she isn't one of my students and if I insisted she use Prof. French it implies more formality and hierarchy than I'm comfortable with. When she refers to me when speaking to students she says things like, 'you need to see the instructor' or 'you need to talk to Mr. French.' both of which are fine with me for the same reasons as above.
So in most cases it might be a simple answer but you really need to have more context to guide you whether it comes from the culture or the institution.
Now, if I can only figure out what to call the other faculty now that I am one...
In my opinion, I don't think it's appropriate to call or act as a professor without PhD because it lead the community on the wrong way of perception. For instance I have a MBA, and sometimes universities invite me to give lectures. The students used to call me as I'm a professor and I refuse because it don't make sense. I know many colleagues haven't a PhD but they are professor. It seems unusual and inappropriate even assistant or associated professor.
In the USA, The title of Professor is given to people that have a PhD and are teachers at any academic level. A person who is a Doctor is someone who has finished a terminal degree meaning they have completed the highest degree in their field of study above a bachelors. Currently a Masters of Fine Arts is the top degree for artist in the USA technically can be called Doctor last name. Art classes are informal setting so you call the instructor by their first name but they are currently trying to develop a PhD program. Master levels are called Instructor. Now because some people get in a snit about the title of Doctor the custom is to only call people with PhD's Doctors. If you are a grad student and are called professor you should correct the person because it is a title that people earn with an additional 5 to 8 years of study. As to the OP on the first day of class the professor should of introduced herself and what degree she has from which schools. Teaching at a 2 year community college only requires a masters degree 4 year universities you need a PhD or terminal degree such as in art person. grads teaching under a direct supervision of of the proper degree person. It was a long answer but so much misinformation in the thread. I have a MFA you will find that most people teaching with an MFA a university know the details because we are the lowly Instructors among the Professors.
As far as physics goes, any PhD hired to teach is rightfully called "Professor." However, their title may technically be, for instances, "Assistant Professor" or "Associate Professor." One is considered a (Full) Professor once one has been granted tenure by the appropriate committee.
In short, one is a professor if one has been granted a PhD and one has been hired on to teach. One is considered a full professor if one has been granted tenure by senior faculty.
That said, I've never met a professor that objected to being addressed as "Dr."
BU has a very nice general breakdown.
EDIT: not sure why I'm being downvoted. If you're an American physics student whose experience is counter to my account, please do share.