All P&G career applications involve a personality test, reasoning test (structured somewhat like a very short IQ test which you can't really prepare for), and interviews. I first applied to the FACT program, which is a week long P&G "boot camp" with the finance, accounting, and tax department, where prospective interns familiarize themselves with different lines, the company as a whole, and life in Cincinnati. You are also given the opportunity to network with new hires, current interns, and upper management, including the CFO. On the last day, you are given another reasoning test (to make sure you didn't cheat on your FACT application), and back to back interviews. Before your interview you will receive plenty of guidance from P&G employees, who will give you tips and cheer you on as you approach your interview date.
The interviews themselves are generally very casual and friendly, although it really depends on the interviewer, like any company. Interviews are completely behavioral, and interviewers are given a list of questions they could ask you. They take notes based on attributes that they are testing you for: "Power of mind", "Power of people", and "Power of agility." Some are more conversational and try to make the interview as easy as possible for you, and others are the opposite. All interviewers expect you to answer questions in the "CAR" format, which stands for Context, Action, Result. This implies a brief explanation of your experience, what you personally have done to solve the problem, and what the result was. Examples can be drawn from school, previous employment experiences, volunteer opportunities, and even personal anecdotes.
Afterwards, it took about 2 weeks before they called me to give me an offer, which is contingent upon a successful hair follicle drug screen, background check, and medical examination. The process after the offer can take several months depending on human resources (I received and accepted my offer 2 months ago and still have not received details on the contingencies), but the full internship assignment complete with manager, role, and brand will be given several months before the start of the internship. You do get to preference a brand and role for your internship, but past interns say that your position is mostly dependent on business need, not your preference. P&G offers more flexibility with full time offers, though. Current employees will contact you and make themselves available after your offer acceptance if you have any questions.