My short story is called "Bad Beat For Aaron Burr," and its iconic hero, Ray Cazador, is essentially a skip-tracer who follows people to alternate Earths and brings them back alive. It's set in an alternate where Aaron Burr pulled the trigger on the 1806 plot, and in which that plot was not the detaching of the West as an independent country (which it most likely was) but an invasion of Mexico, which succeeded in this history because otherwise there wouldn't be much point in setting a story there. (British gold, Spanish fecklessness, criollo opportunism, if you're wondering how it might have worked.)
But one thing I didn't want to do was the standard "As you know, Bob" moment in which one character explains the alternate history to another character. It might have fit in an introductory scene, but I cut that scene because it slowed down the story. It certainly didn't fit in the story itself, nor could I have Ray Cazador look thoughtfully at a world map, read a historical novel, or do any of the other marginally-clever things alternate history fictioneers have their protagonists do so that the audience can get its uchronial rocks off.
Instead, I dropped little bits of the history into the story, hopefully causing a world to emerge from the tale in organic fashion. I only riff on the alternate itself when it specifically plays into my hero's tactical decisions on the ground; here's how Cazador explains how he knows where to find the fugitive, poker-fiend Troutman:
For example, a key rule for cross-world fugitives is: “Stay away from your past.” Not just your personal past – finding out what Mom is doing on this Earth is a great way to get rattled and get caught – but your Earth’s past. For some reason, runners stop and gawk at places that aren’t famous on their new Earth, wide spots in the Potomac marshes where the Lincoln Memorial should be, that kind of thing. On this Earth, France wouldn’t give a statue to the whipped-dog United States when it could kiss up to the Empire that Aaron Burr had built in Mexico. So this New York had a casino in the old fort on Bedloe’s Island, and Gustave Eiffel’s Statue of Fraternity stood in Veracruz harbor. But Troutman wouldn’t be in Veracruz, or anywhere else in El Imperio Mexicano. For one thing, Troutman didn’t speak any Spanish. Troutman’s politics probably ruled out the Confederacy, which was even poorer and more insular than this Earth’s United States anyway. It wasn’t impossible that Troutman had already gone north to Canada, cut a deal with the British. But not likely. In Troutman’s place, Cazador would want the security of “neutral ground” to negotiate any deal like that. And Troutman would need to get his legs under him in the new Earth. He’d be looking for something familiar and safe: poker.
As you know, Bob, Burr's Mexico must bend all its foreign policy energies to weakening and (ideally) fragmenting the United States, a program with definite European approval and assistance. Note the Confederacy, the "whipped-dog United States" (poor and insular; the story mentions New Dollars, a quarter with James G. Blaine's head on it, and puts a casino on the quondam Liberty Island) and the continued presence of the British in Canada. Later on (as Cazador attempts to figure out a foe's accent) I imply that Cuba and Guatemala are provinces of Imperial Mexico, neither one much of a stretch.
I remain tricksy about whether the alternate-world travel includes time-travel; whether the alternate worlds have "alternate presents" too. (Technology is meant to sound slightly retrograde, but not utterly primitive.) Mostly because the story doesn't need me to mention it. If I were to write a whole bunch of Ray Cazador stories, I'd probably have to have one that turns on that point, or more likely just explain it in an introduction. Which I'd probably call "As You Know, Bob."
As you know, Bob, Burr's conspiracy included a number of young, ambitious frontiersmen such as Andrew Jackson and Sam Houston. Just as in our timeline, they prospered when given ridiculous amounts of executive and military authority. The antagonist's name is: "Don Vicente Teodoro Garcia Estancia y Jackson. Mexican near-royalty then. Then Cazador read the printing above the name: Ministeria Confidential de la Emperador. Don Vicente was near royalty in more ways than his blood: he worked for the Confidential Ministry of His Imperial Majesty Aaron IV Burr."
Later on, we speculate about how to get out of New York:
Extracting Troutman by train would take too long: hours to get to Colorado and the Imperial border. Hours in which anything could go wrong, including another border crossing into the nervous, touchy Columbian Union at Youngstown. A car or truck had the same problems, compounded by the grim prospect of an undignified road trip across a parochial, backward countryside full of people who sullenly resented Imperial Mexico.
A successful Burr Conspiracy isn't going to defuse Midwestern secessionist spirit. Rather the opposite. I suspect the Columbian Union separates during the Civil War (which might well have come earlier, with no Mexican War to offer the South hope for expanding slavery) or perhaps during whichever war it is that inflates the U.S. economy enough to demand "New Dollars."
And one last bit, a list of plausible Great Powers:
As the guards fell in behind them, Cazador turned to Don Vicente. Now was the time to damp that frustration, to give him what he wanted: an explanation. In a conversational tone, Cazador said “Moscow.” France and Britain too easy to check, Japan too outré. The Russians seemed like the right touch.
Defeat in the Napoleonic Wars isn't going to end Britain; Japan's rise makes sense regardless; Russia remaining a Great Power likewise.
And one or two things I just threw in for alternates' sake: New York accents are "more Irish-Italian-Breton than Jewish-Italian in this world." That's because I assumed a victorious Bonapartist-Republican France begins encouraging the monarchist Bretons to emigrate. I never did explain why the Jews don't go to America en masse (although I do have one Jewish character in the story's New York); probably the independent Polish Republic/Kingdom of Poland (depending on exactly how Vienna goes in this world) makes the intelligent decision that its most literate, productive citizens should stay there and improve the tax base.
There's a couple more bits of that history in the story, but that should be enough to get everyone started.
1) The first was "Ring Around the Sun," the introductory fiction for Secrets of the Ruined Temple.