Unfortunately (and ironically) I am in the middle of writing a paper almost exactly on this subject (and procrastinating by redditing), so can only give you a brief overview.

Part of it is due to inheritance and gains made prior to the 18th/19th centuries. The areas of Cleves/Mark were inherited by Prussia before the start of the Napoleonic wars, similarly, Ansbach was held by the Hohenzollern family (though it was consumed by Bavaria following the Napoleonic Wars).

The post-Napoleonic "Concert of Europe" was another major factor. Napoleon was essentially a giant etch-a-sketch when it came to the states that made up modern day Germany. This was the Holy Roman Empire in 1789, it was made up of a myriad of different states, the number of which I honestly can't remember or can easily find, but it was a lot. After the Napoleonic wars, however, when restructuring the European balance of power, Prussia's territory in the rhineland grew substantially, here is a comparison picture for the German confederation, a political organization that gave Austria hegemony over the other 38 German states. (There were 39 states within the confederation.)

Fast forward to 1864 and we see Austria and Prussia working together in a war against Denmark for the Duchies of Schleswig and Holstein, the war is over quickly, and the duchies are divided between Austria and Prussia. Two years later, this becomes a point of contention, used by Bismarck to create war between Germany and Austria. In 1866 Prussia and Austria go to war, and the Federal Army of the German confederation, joins the Austrian side (though a number of these states intentionally dawdle, such as Baden) under Bavarian leadership. The war lasts only 6 weeks however, and saw a devastating Prussian victory. Many northern German states, such as Hanover, were directly annexed, and others joined Prussia's "North German Confederation", retaining nominal independence.

Four years later, understanding the need to bring the South German states into the fold, but knowing that 1. France would never accept Prussia dominating the southern states, and 2. the southern states didn't exactly want to be dominated, Bismarck engineered a war with France. Falling right into Bismarck's diplomatic trap, France declared war on Prussia (Using the diplomatic insult casus belli), which prompted the southern German states to join Prussia in the war. Following the war, in which Prussia was very victorious, Germany was proclaimed in the Hall of Mirrors in Versailles. The interesting thing about this Germany is that it was not exactly an annexation of the southern states. The Kings actually retained their titles, especially the Bavarian King, but now the king of Prussia was the German Emperor. Also of interest is that the new Empire did not exactly have a unified army. The Kingdom of Bavaria, for example, retained its own army all the way until the end of the Second Reich.

Anyway, the above is a major simplification, especially in regards to the diplomatic machinations of Bismarck and the constitutional status of all the minor kingdoms that later formed the German Empire. But, I do hope it answered your question, it was partially through diplomacy, partially through war; some of it was annexation, some of it was 'vassalization'. I highly recommend reading Geoffrey Wawro's Austro Prussian War and Franco Prussian War books. If anyone wants more sources or has questions, let me know.

I highly reccommend that you pick up and read Iron Kingdom: The Rise and Downfall of Prussia, 1600-1947 by Christopher Clark, it is considered to be basically the bible of Prussian history.

In my own attempt to somewhat answer the question, the Prussians fought three different wars that eventually lead to the formation of the German Empire. The Second Schleswig War, which was Prussia and Austria fighting Denmark, with one of Prussias aim was to liberate Holstein from the Danes, a largely German speaking region. The Austro-Prussian War, which was a war between Austria and Prussia over which one of them would eventually dominate a unified Germany. Prussia won. And finally, the Franco-Prussian War, a war between Prussia and France, which was considered to be the last straw that lead to the German Empire forming. One of the most important aspects of this war in particular is that the threat of French aggresion, French animosity towards Prussia and Germans, was pivotal to Prussia convincing the southern German states to join forces with them against France, and eventually unify.

All of these were made possible by decades of diplomacy by both Prussia and Austria, as they struggled to re-piece the Holy Roman Empire into a new, unified German state. Prussia and Austria formed the German Confederation after 1815, but neither wanted to subvert control over German states to the other, so it never took off until Prussia came out on top. In the end, much of Prussia success in unifying German states was the result of Bismarcks diplomacy.

Seriously, read the Iron Kingdom. If you like Prussia, you'll love the book.

This thread has generated a great deal of comments that are off-topic discussions of the Europa Universalis or Victoria game franchises.

Yes, someone wrote about Diplomatic Insult Casus Belli in their answer. If you get the reference, please quietly smile to yourself and refrain from creating a post about it in this thread. We have already deleted dozens of such posts, and will remove any future ones. Maybe go and talk about it at /r/paradoxplaza.

Please keep the discussion here historical.

I'm not entirely sure why everyone's ignoring the 18th century part. Silesia, one of the major coal-producing regions of Germany, was gained through the Silesian wars with Austria in the 18th century. Large parts of Poland (much of which was given to Russia post-Napoleon) were gained through the polish partitions at the end of the 1700s, notably the stretch of land connecting Brandenburg with East Prussia (royal prussia, or what in the 1920/30s was the Danzig Corridor). Land was also gained from Saxony at the closing of the Napoleonic Wars, as the Saxon king was seen as pro-Napoleonic.

What happened to the state officials in the smaller states? Were they moved around? Replaced by Prussians? Retrained? To what degree did laws change in the smaller states? The relationship between the states and the Empire has been unclear to me--Bavaria famously had its own army right up until 1918, but during war time it was effectively under the control of the federal, imperial army. Can someone help clarify how these relationships worked, what happened to the bureaucrats?