A script reader's duties entail reading scripts that have been submitted to the studio or production company and writing coverage, which is a specialized industry template that includes a summary of the film's plot, an evaluation that describes why you did or didn't like it, and a breakdown of ratings -- poor, fair, good, excellent -- of such script components as character, dialogue, and story. The reader then decides whether or not to recommend the script and/or the writer; often a reader will recommend the script for purchase for commercial reasons, but will not recommend the writer; similarly, there are times when a reader will pass on a writer's script for commercial reasons, but will recommend the writer for consideration for future assignments. Finally the reader passes the scripts that fall into the recommend pile along to the next rung up the ladder. Although these jobs are hard to get (and don't pay terribly well to boot), there is no doubt that you will learn volumes about the industry's tastes and simultaneously receive an irreplaceable education in the craft of screenwriting by getting a chance to do nothing but read and analyze scripts for the better part of your working day& and night, as is often the case.
If you can't get a job as a script reader, you should try to get a job doing anything industry-related. Log on to everything from studio websites (run a Google search under their names, i.e., Universal Studios, Paramount Studios, etc.) to Craig's List (www.craigslist.org), the latter of which also features actual writing jobs that, depending on the samples and experience required, you might actually qualify for. Do whatever you can to get your foot in the door all while continuing to develop your craft as a writer; just remember that if you have the requisite talent and drive, the rest will follow.
Probably the best way in which you can help your professional cause -- particularly if you are a recent college graduate and have some way to make the financial side of an unpaid internship work -- is to accept a low-level job in the entertainment industry. Hollywood lore is replete with stories of famous careers started in agency mailrooms, although most of these people wound up on the business end of the business. For an aspiring writer, there is no better place to begin a career than as a script reader for a studio or production company.