Warning: Wikipedia contains spoilers
The point of divergence is 1862, the American Civil War. In OTL (alternate-history lexicon for "our timeline"), a Confederate messenger lost Robert E. Lee's General Order detailing his plans for the Battle of Antietam. The orders were soon found by Federal soldiers, and using them George McClellan was able to defeat the Army of Northern Virginia.
In Turtledove's novel, the orders are never lost, and McClellan is caught by surprise. Lee forces him into battle on the banks of the Susquehanna River in Pennsylvania and destroys the Army of the Potomac in the battle of Camp Hill. Lee goes on to capture Philadelphia, earning the Confederate States of America diplomatic recognition from Great Britain and France and winning the war.
In 1881, James Blaine has ridden a platform of anti-Confederatism into the White House. Both American nations are sanctioning Indian raids into the other's territory, and the international tension boils over when Confederate President James Longstreet, desiring a Pacific coast, purchases the Mexican provinces of Sonora and Chihuahua. Blaine uses the "coerced" purchase as a casus belli, and what will later become known as the Second Mexican War erupts.
The novel uses historical figures exclusively for its main characters.
Thomas J. Jackson, old "Stonewall," is the General-in-Chief of the Confederate Army, and ready and eager to strike at the Yankees once more. Among the Yankees ready to strike at him are Colonel George A. Custer, a frustrated cavalryman serving on the Great Plains, and a wealthy, patriotic young Montana rancher named Theodore Roosevelt. General Jeb Stuart has been tasked with defending the new Confederate territories from the Yankees, and from the native Apaches, led by the venerable holy man Geronimo. Frederick Douglass, a former slave and a fiery orator, observes the Union forces at war, along with Alfred Schlieffen, the German military attache to the U.S. Observing from the sidelines in San Francisco is Samuel Clemens, a sharp-witted newpaper editor. And flitting about North America is the man some say started the whole mess: former President Abraham Lincoln, now an orator struggling to keep the Republican Party united in the cause of the working man, against the Democratic Party and Big Business. And if the Republicans prove unable to meet the challenge, he'll find someone who can.