Applying as a Graduate Student
If you apply to Stanford as a graduate student in psychology, you should determine which area (or areas) of psychology to apply under. Five areas admit students: affective, social, developmental, cognitive, and neuroscience. I am primarily affiliated with affective and secondarily with neuroscience. Together, these areas can admit from 10-12 graduate students a year.
The faculty within an area split grad students, so affective typically admits 2-4 per year. However, there are at least twice as many personality faculty (~8) as admits per year, so one student typically joins our lab every other year. Part of this limit has to do with the fact that all admitted students receive four years of funding, and thus do not have to rely on grant support. The graduate admissions administrator, can answer detailed questions on the application process.
Alternatively, you could apply to Stanford as a neuroscience student. There is no neuroscience department, but there is an interdepartmental neuroscience consortium. This program also admits approximately 10-12 graduate students a year, but those students are shared among more faculty, due to the interdepartmental nature of the program.