Explaining Shakespeare

I often open up a word processor and try to bang out some notes on the general topic of what I’d call “explaining Shakespeare.” I know that No Fear and For Dummies and Sparknotes have done the subject to death, but I like to humor myself and think that, if I ever find my hook, I could actually add some value to that particular canon.
I get stuck over and over again in the same spot, however. So I thought I’d open up the idea to discussion. Here’s my dilemma. When you are attempting to explain a Shakespeare play (let’s say Hamlet), how do you do it? Do you describe the chronological events of what’s happened / happening? Do you describe it scene by scene? Or do you talk about the characters, and their relationships and motivations?
The easy and done to death answer is to go scene-by-scene. I don’t like this, though, for a couple of reasons. Most notably, every production is different. I hate the idea of telling somebody “Ok, in the next scene Polonius is going to send Reynaldo off to spy on Laertes” and then have them go to a production where that doesn’t happen. You know what I mean? Most people who want to read a summary of Hamlet aren’t necessariy going to then sit down and read the text (except maybe high school students :)). Grown ups who want Shakespeare explained to them want to understand the story, so that if they ever see it they know what’s going on.
So then what about chronologically? I like the idea of starting out talking about Hamlet being off at school, and his father dying. I think that this is something that many families today can immediately relate to. But … then what? How do you go from “Hamlet’s dad died” to “Horatio confirms his ghost walking the castle” to “Laertes returns to France” and so on through the play? You can find a way to do it I’m sure, but it’s going to seem fairly awkward (since there are places in the play where the timing itself is a little suspect anyway), and the harder you try to make it work, the more you’re going away from the story on the stage so that if someone does go see a production, they’re just as likely to be lost by what’s happening. You’ve ended up writing an alternative version of Hamlet. A novelization, almost.
Lastly there’s the idea of character study. While I love this idea, I love taking Hamlet and just walking through the entire play completely from his point of view, I think that this simultaneously provides the most interesting story while also offering the least immediate value to the audience. Make sense? I don’t think my reader wants 400 pages on Hamlet’s relationship problems. My reader wants enough information about the story that they will both *understand* it as well as *enjoy* it. Going too deep into each character (and really, how can you not go deeply into each character if we’re talking about Hamlet?) is going after a different audience. That’s like the second-stage audience, the ones who have already seen and understood and enjoyed Hamlet and now say “I’d like to learn more about these characters.”
What to do? How do you explain Shakespeare to somebody in a meaningful and useful way, without resorting to a scene-by-scene translation?

(As I write this, I think I know my answer. I’ve gone to see Shakespeare with people casually. People who don’t know the story. So they ask me, “What’s it about?” And I proceed to tell them, to the best of my ability, what I think is a useful description of what they are about to see. What I need to do is record one of those spontaneous explanations, and then write it down, and go from there.)