I hand submitted an application. These can be obtained in store or on their website (no online submission, unless for SM/DM level positions).
Hand in the application yourself. When parents would hand in applications for their 17, 18, EVEN 19 YEAR OLD "children," I would immediately consider them a "last ditch effort." Having someone else hand in your application demonstrates that you have little responsibility, and in general don't care about the job.
I called the store for a followup after one week; if merited, call back again every other week.
I dressed casually for the interview. The dress code at GameStop requires you to wear a polo, sweater, or collared shirt. Regular t-shirts are allowed if provided through promotional kits. Jeans or khakis are fine with sneakers / dress shoes; no shorts and no sandals. Loafers are allowed, although upper management may decide what you can / cannot wear.
In other words, dress for the job.
I was asked my previous experience, my familiarity with consoles, game genres, and customer service. The important factor is how well you can / cannot deal with other people. It is also important how well you can sell. Knowledge is perhaps the least important asset, and if anything, will be considered last.
Too often would neckbeards, forever alones, and other gaming "enthusiasts" apply for positions, only to be denied following interviews. GameStop does not care how quickly you played through Demon's Souls. Your opinion on why the XBOX 360 is better than the PS3 is moot. How many consoles you own, and games you play a week is depressing. These will not help you get the store a profit, and likely will only annoy your socially competent coworkers.
Any and all gaming knowledge can / will come following your hiring.
Be cool, calm, and collected, in order to demonstrate you are competent at alphabetizing, using a POS system, and talking to human beings that aren't digitized.