“An internship is a way for graduates and students to gain experience. This places an obligation on you, the employer, to educate and train them. An unpaid internship can last no longer than four months, with the intern moving round the company, experiencing a wide range of differing positions with no onus on them to produce work for your company. An internship, to be unpaid and legal, needs primarily to be a learning and training experience for the intern. You should not expect the intern to produce work that is going to be of benefit to you.”
Quoted from: Can I legally hire unpaid interns? — useful if offering internships (to stay on the right side of the law), and if seeking a placement (to ensure your chosen internship is the best possible match).
That’s how unpaid internships should work. It’s why I was more than happy with mine.
If you are searching for a design internship, this AIGA listing might help (US-based opportunities).
Somewhat related is this nice read from 2009. It’s Andy Chen’s blog entry about his summer internship with Paula Scher’s team at Pentagram. I wonder what he’s up to now.