Just as in the OTL, the pretext for the war was the same: Prussia and Austria had a dispute over the administration of Schleswig-Holstein. The invasion proceeds the same, also. The Prussian soldiers, under Moltke, invade Saxony and the Czech lands. The Germans, after a swift mobilization, catch the Austrians at Sadová and inflict a devastating victory: 9000 Prussian soldiers are killed, versus nearly 45000 Austrian dead. Bismark, at this point in the OTL, is ready for peace, and within three weeks, in the OTL, it was signed at Prague. However, this is the POD. Bismark decides to push for tougher terms from Austria.
The Prussian armies continue pressing deeper into Austria, and by July 19th have reached the outskirts of Prague. While the Prussians surge deeper into the Austrian heartland, he Austrians regroup, and the two armies clash at Gaweinstal. Again the Austrians are routed, and this time, with morale disappearing, thousands of Austrian troops are captured. The Prussian army presses onward and encircles Vienna.
Meanwhile, the Bavarian armies are, over the course of several battles, almost completely annihalited. The king of Bavaria, Ludvig II, is killed in combat. With leadership gone, the Bavarians sign a peace treaty. With no heir, one of the terms is recognizing Wilhelm I, king of Prussia, also as king of Bavaria.