Aside from that my exposure to the original series is pretty minimal. I've seen scenes from multiple episodes, but I don't believe I've ever sat down and watched one in its entirety. I've avoided all the films with the exception of a few scenes from The Wrath of Kahn and The Voyage Home. In fact the only Star Trek film I've actually seen all the way through was First Contact and that's only because my college broadcasted it on the university-only movie channel (which appeared to just be someone showing DVDs and was apparently not legal since they stopped showing them in my senior year and just gave us HBO). I've seen a number of episodes of The Next Generation since I was fairly into it when I was younger, though even then I think I was watching reruns.
Point being that I have no real attachment to Star Trek as a franchise. When I heard J.J. Abrams was directing a series reboot I admit I was intrigued since I will apparently watch anything he is involved in (except Alias somehow, though saw an episode of Felicity once) but I didn't really put much thought into it beyond the initial intrigue.
So anyway, after an impressive trailer and a massive amount of internet-based hype, I decided it was time to break my Star Trek motion picture cherry, so to speak. Actually the trailer was enough to make me want to see it because it ended up looking awesome instead of boring, which I think is an important quality for any movie to have. The internet-based hype was an added bonus to get me to see it sooner and avoid being spoiled (spoiler: I was minorly spoiled a couple of times anyway). Nicely enough the movie rather obviously sets out to reboot the original series timeline. Due to some involvement with time- travel (J.J. Abrams apparently cannot stay away from it) one of the characters even comes out and says, almost as bluntly as possible, that the events are occurring in an alternative timestream, Back to the Future style (they don't say that last part of course) due to events early in the film. So because of that fact the new viewer will have no major problems jumping into it even if they don't really know much. You're introduced to most of the major characters with little difficulties though the movie itself is rife with references to the original series.
It's these references that makes me wonder how difficult the film would be to pick up for someone with very little knowledge of Star Trek. Things like Bones' "damnit I'm a doctor" lines or Chekov's goofy accent or the guy in the red shirt getting killed or Kirk making out with a green woman or any number of things are a pretty big part of what makes the movie so enjoyable and would be totally lost on someone like my grandma who probably hasn't seen a single episode of Star Trek. Of course someone like myself who also has no first-hand experience with the original series comes to realize that perhaps Star Trek is actually a massive part of our culture at this point. I've never really seen an episode, but strangely I know a huge amount about the series, apparently. Maybe it's because I saw the episode of Futurama that featured almost all of the original series' main cast, but it has become apparent that it's ridiculously hard, if not impossible, to escape viewing almost any media without falling on a Star Trek reference. It's not something I expected, since it never seemed to be as mainstream as something like Star Wars, but I guess it turns out that it secretly is.
Weirdly enough the movie is extremely light on plot, which is perhaps a good thing. Whereas Star Trek can have a tendency to dive into pseudo-science and take itself too seriously which can lead to long-winded discussions and debates by the characters, this film never really falls into that trap. It concentrates on the characters and their relationships, and does an amazing job. You could probably summarize the entire plot of the film in a few sentences, and yet the substance outside of that plot is where it truly excels. The casting and performance of every single actor is also exceptional, as Abrams seemingly has a knack for getting the most out of his actors. If you were expecting Dawson's Creek In Space (which is one complaint I heard mainly when the casting for Kirk as announced) you will be sorely disappointed. The film dances on the line between campy and serious in pretty much the perfect amount, and with enough references and nods to the original series to keep probably any fan happy (though I could be wrong there).
It's not without some issues, and I could really get into them, but they'd be fairly minor quibbles at this point. Spock's romance comes across as forced and almost weird, but that might just be because Spock is kind of awkward. Certain events of the film seem to be taken almost too lightly by some characters, and are juxtaposed with other characters almost absurdly overreacting to the same events. Still, minor problems that I had no real issues overlooking. Overall I have to say I had a great time and for the first time in my life I can't wait for the next Star Trek movie. Highly illogical how that worked out.