Applied on the internal website/database job website with the usual CV, motivation letter and other basic info.
It was an intern position during my last year of master of science in Finance. The position description was very detailed and comprehensive. Later during the actual internship I did actually all that was described there. Later I understood how important it is for all parties involved in the recruitment process to be straight forward and transparent.
The first interview consisted of direct initial contact with the manager and the person I would support (no HR). Basically it was a background check with questions ranging from motivation for the area of interview (operational risk management in an asset management company), skills, past studies and expectations. The manager was very clear in the objective of the internship hire (6months) with the possibility for a temp contractual hire at the end. The people were nice and made me feel comfortable.
I would recommend to try and find as much as possible about the job expectations directly from the people that you should work with. If the manager is not clear and exhaustive about job descriptions and expectations then ask ask ask. There should be a mutual fit between the interviewer and the interviewee.
The second interview was quite similar but with other people I would interact during the internship. It was more a confirmation interview checking for second opinions.
I was very eager to enter an asset management company so I prepared well about industry, company, corporate structure, fresh news, risk management in general and current issues and directions. The office people seemed very nice and the trip in the elevator was definitely not awkward.
I was called and offered the internship in an hour after the second interview and started in a few days.