I contacted the professor I was interested in working with by email. Simultaneously I submitted the grad school application to the Prof's department, and specified his name as first choice. A while later (1-2 months) they contacted me to schedule an interview. The interview I met with 4 or 5 profs including my first choice. There were 10-15 other admitted prospective students. It was a pleasant process. My advisor did most of the talking during our meeting time. This was my first interview really so I was not particularly savvy about the questions I asked.