It's going to be tough to get a job with the Jets because so many other people want one - that's why interns are unpaid. To get a job you have to stand out from the crowd and, with so many applicants, the employer will be looking for reasons to just discount as many applications as possible as quickly as possible. A single spelling mistake on your introductory letter would be enough because there will be many, many letters with no spelling mistakes. Therefore, the advice offered here has all been relevant because you can't afford a single mistake in this kind of thing. To stand out you need to prove you are serious. Having a blog that is updated regularly would show commitment. But to stand out from the other blogs run by other applicants it would need to be well written and, again, mistake-free. Other relevant experience would help, such as an intern stint at another company - a letter of commendation from a previous employer would be useful. After you have something to show off on your CV, use the avenues shown by others in this thread. Mangini worked his way up from nothing so it's not impossible, but remember his attitude - if he was asked to photocopy a stack of documents he was going to be the best damn document photocopier in the business. Never think that anything is beneath you (as an unpaid intern, nothing is beneath you). Never give them a reason to think you're not serious about the job. Other than that, it should be easy! Good luck.
Funny story, my neighors son graduated with a degree in marketing and held some so-so jobs for a few years. One day he was in town visiting friends in the Atlanta area and they decided to take in a Braves game. Out of the corner of his eye he sees a bunch of guys his age walking through the entrance for corp execs and he starts up a conversation with them, ala "how did you get a job?" They told him to simply submit an application and take it from there. 3 years later he's the director of corp sponsorship.