Film festival acceptances are difficult to gauge. That's why so many people refer to film festivals as crapshoots. While there is obviously a certain level of artistry in most shorts accepted into big name festivals, there's always an aspect of chance, which makes it seem capricious, especially when Sundance only accepts 50 some odd american narrative shorts a year. What separates the 50 accepted from the other 50 worthy films that barely missed out? The point is that there's no magic bullet. You can't try to make a trendy film and hope it gets into sundance. That's why the Tarantino rip off has become a mini-genre.
In terms of logistics, getting into a festival, any festival, (besides the fact that story is probably most important, followed by acting), it's best to follow the advice people have given about organized submissions. This doesn't mean that your DVD screeners have to look like DVDs you'd by at Amazon, with fancy artwork. Just make sure they're clearly and professionally labelled. Also, submit to festivals early. Acceptance committees get bogged down near the late submission and notification deadlines, and you'll get a more 'fair' view if you submit early when they're less stressed.
Also, don't forget about sound design. Some people brush it off, but it's something that you can control that will make your film better and increase your chances. Also, make sure your editing is crisp and professional. Good editing is something subtle in postproduction that can help you film be received more seriously.
Also, familiarize yourself with the reputations that festivals have. Look at the rosters and synopses of films accepted. New York Underground Film festival accepts different films than Tribeca than Sundance than South By Southwest than Cinematexas. This isn't something to do at the script stage, but after your film is completed, make sure you're not wasting your money on festivals that aren't geared towards your film. Also, people pursue different strategies with their shorts. Some try to build up acceptances and awards at small fests to get more cred when they enter into larger fests (if your film wins a bunch of awards at second and third teir fests, it may get a better, more serious look at the big oness). Others try to submit to the big ones first, maintaining premeire status and hoping that they'll get in and then have others knocking on their door. With sundance it might help to have premiere status. Another consideration with sundance is that films shot on 35mm have a higher acceptance rate. Does this mean that they take films shot on 35mm more seriously than films on DV? Not sure. It's probably just a corollary. If you have the time and money to shoot 35mm, there's a better chance you've put time and consideration into the script, acting, cinematography and didn't just wing something with your friends and dog. It's an interesting statistic.
Keep in mind that Sundance is not a golden ticket. People (most people) go to sundance every year with shorts and don't get anything tangible out of it (agent, feature deal, commercial directing). That's why so many people have told you to forget about sundance. It's not that they're trying to kill your dream. It's just that you can't control getting into Sundance by dreaming about the mythical Sundance. You have to make the films you're compelled to make, learn from your mistakes, progress, and be realistic about what film festivals like sundance can and can't do for your career. That's not to say that you shouldn't do everything in your power to push the odds in your favor, but you'll be swinging at windmills if you just focus on what Sundance wants and not what works in your film. I'm sure they get a zillion films a year trying to rip off the latest trend, whether it's memento, tarantino, or the fat white guy doc expose.
Finally, check out
http://www.withoutabox.com. They make submissions easier, and you can learn a lot about the process on their forums.