I identified a post from a then-current intern on an informal Facebook group for students of my university. After I sought some basic information about the position from the intern, I applied by sending my CV and other relevant documents directly to the supervisor.
Upon being invited to interview shortly after (perhaps two weeks), I traveled to the interview location (HQ) and met with the manager who would later turn out to be my supervisor. He invited me to a drink at the coffee bar, and we sat in the corner of a relaxed location to carry on with a discussion.
The interview was mostly relaxed, and I did not have to explain much about my knowledge of the company or sell my passion for the industry - it was thus more focused on my personality, interests, skills, and experiences. Travel costs were reimbursed.
I later heard from the then-intern (the one who posted the position) that I made a good impression. I sent a thank-you email to the interviewer and received a response shortly after indicating that there were still some managerial decisions needed to be made prior to any definitive offer or lack thereof. I was a bit persistent (but friendly and appropriate) in sending a follow-up email about one month later. About two or three months after the interview, I received an offer to start at any point between four and ten months in the future - I appreciated and was impressed by the preparation and flexibility.
I accepted then, and my supervisor agreed to a 4.5-month internship although their hope had been for 6 months.