In most graduate creative writing programs, you can focus on either fiction (me), poetry, or creative nonfiction. The MFa is a terminal degree and has been for many decades - meaning that universities that require you to have an advanced degree for a teaching job will hire you if you have an MFA - but increasingly popular is the creative PhD, which exists at about 35 schools in the country.
At the core of these programs is the writing workshop. Although you take other classes, mainly in literature, you spend about half of your time in workshops. These classes are small - usually 10-12 people - and while they include discussion of published work, the most important element is discussion of one another's work.
I'm about two years post-workshop (having graduated two years ago next month), and in the shower the other day (where I, of course, do my best thinking) I was musing about the workshop experience: what am I glad to be done with? what do I miss, even if just a little?
Sitting through a workshop of your writing is about one of the most soul-draining things I can think of. (But it does not even come close to law school.) You must remain silent while your classmates criticize, challenge, misinterpret, misunderstand, and attempt to change every last aspect of your work (sometimes, it seems, down to the name of the author).
At the very end, you are permitted to ask a question or two; of course what you really want to do is mount a WWIII-size defense of your work and then launch a nutso offensive - flame throwers, UZIs, the whole shebang - about what careless readers your classmates are, how they're ideas don't make sense, how they're so stupid and clueless b/c they "just don't get what" you're trying to do. Etc. etc.
Everyone has a bad workshop at some point or other, and it's not a pretty sight. Believe me, I've been there.
That said, a workshop isn't always like that and, even when it is, sometimes something can be salvaged from the steaming wreck.
When your work is critiqued week after week, your skin becomes thicker. It never get thick enough that criticisms don't hurt at all, but after a while you learn to filter and separate out much of the nonsense. You decide whose comments matter and whose don't. Writers whose work you respect, who are good readers, thoughtful, meticulous, open readers - these are the people you listen to. The other commentary, well, you do your best to toss it out the window.
If you can do this - keep what counts and forget the rest of it - you find that you've gotten a rare opportunity. There you sit, with people who have paid attention to your work and taken it seriously; who have the vocabulary to think and talk about creative writing; who have the skills to envision how your piece could become stronger, fuller, more powerful - there you sit, and all eyes are on your writing. It's not a perfect system, and it's always a crapshoot, but sometimes things don't turn out so bad.
And, every now and again, you might just get a comment like this from your prof:
"Your sentences are nearly perfect. They read like Anne Tyler's."
As someone who values the language of writing above all else, I didn't mind reading that one little bit.