The Register had just begun its summer internship program when I was there, and as far as I can tell they wanted interns to apply to one of the city editors. First, I grew up in Iowa City, where the Gazette has a bureau. Being from the area is always a plus. Second, I already had experience with the university paper, The Daily Iowan.
Some experience is another big plus.
You also need some guts, in just calling the paper and seeing if the editors take freelance pieces or have a program like the Gazette correspondent program, where you work by the story. I met this really gruff editor there who did not make me feel any better. I got a very brief tour of the building from someone. The next day, I was basically treated as a regular reporter. There were tons of forms to fill out and videos on workplace safety and sexual harrassment to watch.