/u/Badgerfest is much more thorough in analyzing just how Prussia militarily defeated Austria including Prussian military reforms, etc in this thread from ~9 months ago.
I'll summarize the political events a little though. Austrian and German history is my specialty.
So basically, as said in other threads, Austria was losing power internationally and Prussia under Bismarck was gaining more. Prussia actually teamed up with Austria to capture Schleswig-Holstein from Denmark (with support from most of the German world). In 1865 at the convention of Bad Gastein, the two provinces were placed under joint Austrian and Prussian rule. Austria got Holstein and Prussia got Schleswig. The problem for Austria is that the provinces were geographically far away and much closer to Prussia. Austria was also "financially strapped," so they prepared to give Holstein to Prussia in exchange for areas of Prussian-administered Silesia, which were closer to Austria, but had been won by Prussia in the 1700s (Ozment).
Bismarck refused, ignored the Bad Gastein agreement, and occupied Holstein, also backing out of the German Confederation. Austria drew soldiers from "sympathetic confederation lands" and Bismarck and Franz-Joseph had their war at the Battle of Königgrätz in the modern-day Czech Republic (now Hradec Králové) on 3 July 1866 (Ozment). As you can see from the wiki page, the Prussians won decidedly. They were better armed and had more efficient leadership. From what I've learned, the superior Prussian armaments were quite important to the outcome of the battle. From Wikipedia:
The shorter range of the Prussian artillery as compared to the Austrian was moot, while the vastly higher rate of fire from the Prussian breech-loading needle gun, compared to the Austrian muzzle-loading small arms and cannon were paramount. In addition the needle gun could be operated while prone in defense, and while moving quickly on the advance, while the Austrians had to stand up after each shot to reload their Lorenz rifles.
The Treaty of Prague ended the Austro-Prussian war on 23 August 1866 and dismantled the German Confederation. Schleswig-Holstein obviously went to Prussia. The North German Confederation was established, including Prussia, Saxony, and Annexed Prussian lands of "Schleswig-Holstein, Hannover, Hesse-Kassel, and Frankfurt" (Ozment).
What follows is the Franco-Prussian war, which I can go into a little if needed as well. Basically, Prussia got bigger and France sensed a balance-of-power shift, so they worried, but this is basically Austria's role: losing to their Prussian brethren, resulting in a Kleindeutschland, little Germany, rather than a Grossdeutschland, greater Germany, which would've theoretically included Austria. After the Franco-Prussian war, the German Empire absorbs Bavaria, Baden, and Würtemberg, and, of course, Alsace-Lorraine from France.
Source: A Mighty Fortress: A new history of the German People by Steve Ozment pages 208-211.
If I may give some advice, in case you haven't posted here before: Try to be more specific. The more detailed your question the higher are the chances to get a very good answer from one of the historians here (which I'm not).
Do you mean the founding of the first German national state 1871? the Third Reich or the unification of West and East Germany? (I'm guessing the Third Reich though)
Are you interested in the people's opinion or how the politicians handled it? Do you want to know how a certain situation developed? Or anything else?
This is an interesting question, and others asked similar questions in the past:
As always, no one qualified to answer should feel dissuaded from giving their own answer, or expanding upon previous work. In this case, a couple of the questions were asked quite a long time ago (by Internet standards), and this question today certainly welcomes a more comprehensive answer.