One of the first steps you can take is:

• Visit your university's alumni building or web site. Find out if they have a directory of graduates who are willing to talk about their careers with current students.
• Contact someone in this industry and see if you can setup an internship for the late summer or winter.

If those two options don't work you can also go to the NFL Team Jobs Board website. They have internship offers periodically and give you the information and resources to find out about working for an NFL franchise.