Girl Genius: Agatha Heterodyne and the Perfect Construct is pretty complicated, and no simple overview can cover all of it. But here is a very brief guide to the high points, and the order you might want to read things in.
A General Note: While this wiki is somewhat cleaned-up from the original version, it's far from pretty yet. Be warned that there is still a good deal of discussion and ideas intermixed with the actual game text. The game was being written and tweaked right down to the wire, and it's not nearly in "boxed" condition yet.
Just the Good Bits: Most of the following is intended to give you a good grounding in all of what's going on in the game. But if you just want the author's favorites -- the stuff I most enjoyed writing -- I recommend:
The Plots are probably the easiest way to follow what's going on in this game. Since these pages weren't player-visible, they're messier than some, but they are the threads that tie the various characters together. Here is an inventory of the most important plots, and who they principally affect. Note that there are a bunch of more-minor plots that are more focused on specific characters -- I recommend going through the Plots page to see all of these.
The biggest plot in the game is the Mirror of Amagog and all the chaos it causes. This particularly shows up in the Infinite Agathas plot, as well as the closely-related Agatha Transformed. These plots swirl around all three Agathas (Maria/Agatha, Helen and the Baroness), as well as Artie and a bunch of other characters.
Related to all of that is the Amagog-centric plots. The Prophecy of Amagog centers on Moloch, but really concerns many of the other plots in the game, and the Legacy of Amagog gets into what happens next. To understand the backstory here, you may want to look at the sheet for Amagog himself, as well as the Timeline, which gives you some historical perspective on what has gone on in the past. And then there is the Replicators plot, which is an odd little offshoot of the story.
For the members of the Circus, the principal plot is Circus Arrested, which details why there are only a few of them here; the player's viewpoint of this plot can be seen in the Circus Bluesheet. This also ties into the Stolen Crystal plot, which crosses over into a number of other situations, because the Clockwork Crystal is one of the principal MacGuffins in the game.
For the students from Castle Wulfenbach, the most central plot is the Succession of Holfung-Borzoi, which pulls together a whole bunch of people in the question of who should be the new heir to the throne. There is also the Runaways plot, concerning where they will all go next.
DuPree's principal plot, which hits a few other people, is the rather ornate Brigadoon Effect story. This is probably the most complex backstory in the entire game, and ties closely into a shared history that also hits Z, Moloch and Embi. It is also the story of the Race to the West Pole, which will hopefully turn into a play-within-the-game in a later run. (However -- IMPORTANT -- this plot is likely to be more or less scrapped and re-written, because it didn't work well in practice.)
As for the Jaegermonsters, they don't really have all that much formal "plot" -- that would only get in the way of the chaos. But the Many Jaegers plot discusses what they do have, and the Jaeger Cosmogony and Jaegerkin bluesheets tell you a bit about where they are coming from. (Note that this is known to be non-canonical, but it was fun to write.)
Other plots that pull in a number of characters include the Brain Transfer (a bunch of people scheming to deal with the Wulfenbachs once and for all), the Children of Skifander (the story of Gil's parentage), and the sprawling Mirror-World story -- the world as the Baroness knows it. Note that one of the better guides to the plots of the story is the Baroness' character sheet itself: while her world is different in many key ways from this one, she actually knows more about the plots of the game than anyone else does, because she is quite well-versed in her world's version of many of them.
If you've survived trawling through that, I recommend a skim through the other Plots -- there are a number of smaller plots listed there, which concern just a few players. And of course, there are the Characters themselves, which pull those plots together into the actual game materials that the characters received...