Because this was a really good question I decided to give it its own post and push back my short review of my last three reads until tomorrow.
Applicants are asked to submit undergraduate grades, a statement of purpose, three letters of recommendation preferably one or two who have been your prior writing instructors, and the all important writing sample. Some schools ask for GRE scores but those are mostly a formality for acceptance into the Graduate School not the actual writing program. Sometimes they ask for a CV, for secondary essays on your "personal journey"* that brought you to that school or for your teaching philosophy to determine whether you'd make a good TA.
*Aside: My all time favorite is the "personal journey" essay, because after you write it you get to hold hands and skip, then the applicants take turns falling backwards into each other's arms -- all because they've found themselves through their personal journey essay. Ahem.
Despite all these collected bits of information, acceptance is based almost entirely on your submitted writing sample. For fiction programs that means two short stories totaling 25-40 pages (depending on the program). They estimate the writing sample is 75-90% of the admission criteria. Because if you can't write then it doesn't matter that you had a 4.0 from Harvard.
In the November/December Poets&Writers Magazine, there was an article titled something like "Confessions from a former application reader," in which it was stated that the preliminary reader of the application goes straight for the writing sample. If the sample fails miserably nothing else in the application packet is considered. A successful writing sample is generally a demonstration that the applicant is a storyteller. The program isn't looking for fancy technical work because that's what the program is there to teach, they're looking for potential. Again, prior publication isn't necessary because that's what the program hopes to help get you in position for. Another plus always seems to be the ability to establish a strong voice within a short piece, particularly if it is unique to the writer. The kiss of death, however, comes when applicants attempt to copy the voice of published faculty at the program thinking that they're working to flatter. Usually the unnatural assumption of the new voice does more to destroy the story and flatters the faculty like a muumuu.
Applicants get shuffled into "piles" by the preliminary reader and the better ones are then reviewed by a committee, often made up of faculty, program director and occasionally current MFA candidates. Some programs go straight for the committee and skip the preliminary reader. In committee, the writing sample once again reigns supreme. Borderline students are considered in light of their other submitted materials.
Of course, this is not to say that having a lousy undergrad GPA doesn't matter. Most schools require a 3.0 or higher and significant coursework in English or equivalent experience in writing outside of the classroom.
The focus on the writing sample makes the review process extremely subjective, not unlike the publication process -- so, in that respect, it's very fitting -- and almost the complete opposite of the law school application process, which is based entirely on the numbers game (GPA, LSAT, class rank and undergrad school ranking). But at the same time that subjectivity makes it that much more personal: you are allowed to be viewed not just as a name and a number but as a writer with potential for growth. On the flip side, it also makes rejection that much more personal, but we're trying not to think those thoughts just yet.
Note: My answer is gleaned from myriad sources; it is not first hand information and is in no way the definitive answer for any one program.