The process began on-campus during the fall semester, when internship recruits are identified from the juniors in attendance at events. There are multiple events held by various student associations in which KPMG participated, as well as access to interview application through my school's on-campus recruiting web portal. For the interview application, a resume, transcript, and cover letter were required, as well as a suggested GPA of over 3.4. If your application is accepted, you then sign up for an interview slot through on-campus recruitment.
There are two rounds of interviews: one on-campus, and one at the office. The interview on-campus is generally just a 1-on-1 interview, where mostly behavioral questions are asked. There are also other questions -- such as why you seek employment at KPMG, what related skillsets and expertise you possess, what you expect to get out of it, and situational questions. This is usually with a manager or senior manager in the practice. Few, if any, questions are asked about the company in general -- just make sure you know what your practice does, and that you can express it when the time comes.
The second interview (assuming you did well on the first one, of course) is in the office, where you are rotated through three partners, each conducting a 1:1 interview. How this interview progresses is generally up to the nature of the partner. My personal experience pitted me against a partner that seemed more excited about his own experience at KPMG, one that asked me technical questions regarding classwork, and one that carried out an interview much like the first round. After speaking with each of the three partners, you are taken to lunch with the entire pool of applicants, with recruiting co-ordinators, associates, and maybe managers in attendance. This is to make sure that you know how to conduct yourself in a social setting appropriately -- dining etiquette, conversational skills, and how much they like talking to you in a non-professional setting.