Germany kicked France's rear in less than a year, toppled their government, and called for the creation of a new French government which became the Third French Republic.
The tension between France and Germany had been caused, in large part, because of disputes over land around the Rhine river and valley. There were quite a few areas in this area that were inhabited by predominately German speakers and people of German background under French Rule.
The Germany of the late 19th century was very clear about their desire to unite Germans once again. Because of this, there was a lot of tension between the two sides.
The deciding issue happened when a French Ambassador was sent to negotiate with the Prussian King. The meeting was relatively unsuccessful with neither side achieving their goals.
Bismark, who was dead set on going to war, summarized the encounter in such a way that it appeared that a short and curt conversation had occurred between the ambassador and the king. This summary, referred as the Ems Dispatch, was then made public.
From the summary, the French believed that their ambassador had been snubbed and the Germans believed that their king had been insulted. This turning of popular opinion was enough to persuade the politicians on both sides who had originally been unwilling to go to war to change their minds.
Other than that, it was a pretty standard war as far as the time went. Some notable events were the usage of universal conscription (basically, the equivalent of a modern draft), the usage of the telegraph and usage of railroads to move troops around (first time these two had been used on a moderate scale had been in the American Civil War but this war was the first time in which both were used on a large scale.
http://en.wikipedia.org/wiki/Franco-Prussian_War#Summary_of_Military_Events