The program that I applied to at UCSF was the Master's Entry Program in Nursing. The application process for this program included writing 2 essays - one goal statement and one personal history statement - and obtaining 4 letters of recommendation. The application itself was not difficult but what was challenging was applying for multiple nursing schools at the same time. Unlike applying for medical school, nursing school applications are not uniform and actually differ greatly, requiring different essays and pre-requisite classes for each one. UCSF had a different deadline and the number of letters of recommendation seemed like a lot to me at the time.
As far as important criteria for admission, I would say that they are looking for candidates that have a something unique to bring to the field of nursing, rich perspectives or past experiences that they can carry into their new career, and those who have a passion for working with underserved populations.