What do I have to do to get an internship at the New York Times?

I hope to someday intern (and maybe work) at the New York Times, and I am wondering what is required for this? Obviously you need clips and a cover letter and things like that. But is an internship at the Orange County Register and the St. Petersburg Times enough? Plus around ten good clips from a college newspaper? How do I write my cover letter and my "500 word autobiography?" Is it really impossible to get this internship?