A short summary:
This war, fought mainly in German countries 1618-1648, had several causes but it is often described as a religious war between Catholics and Protestants.
It started when Protestant German nobles in the Hapsburg-dominated principality of Bohemia revolted against the Catholic king Ferdinand and the Holy Roman Empire. The first act of violence was supposed to be when Protestant nobles hurled two royal officers through a window in Prague, an event often referred to as "the defenestration of Prague". A full scale revolt ensued and Ferdinand was deposed of the throne of Bohemia. At this time the revolt spread to other Hapsburg dominions.
The Holy Roman Empire and the Catholic League under general Tilly reacted strongly, defeated the Bohemians in November 1620 and began a period of severe repression in Bohemia.
Meanwhile in the Palatiniate (German: Pfalz), the revolt continued under von Mansfeld and Christian of Brunswick only to be quenched by Tilly in 1622. The conflict may have ended there if it wasn't for the fact that foreign powers had noticed the success of the Hapsburgs and feared that the power balance was being tipped too far in the Catholic direction.
The first to react was the Danish king Christian IV. With the support of England he sent troops into Germany, only to be defeated by Tilly and Wallenstein, who retaliated by attacking Danish provinces.
At this point the Swedish king Gustavus Adolphus (Swedish: Gustav II Adolf), who had designs on Poland, began to feel threatened by the Catholic forces as well. A devout Protestant, he also claimed religious reasons for sending troops into Germany. With the support of John George of Saxony, the Swedes defeated Tilly at Breitenfeld securing northern Germany for the Protestant union.
Wallenstein, who had been removed from his command in 1630, managed to get back into the action in 1632 and met the Swedish forces at Lützen. The battle ended with no significant victory for either side, and Gustavus Adolphus was killed leading his cavalry. The Protestant union was left disorganized, even though they were ahead on the battlefields and the Catholic army was all but defeated. The people of the German countries, where the battles were fought, also grew wary of foreign soldiers marching across their homelands and support was low.
In 1635 France entered the war opposing the Hapsburgs and, religious matters aside, the Swedes decided to support Cardinal Richelieu to save what they could of their hold in Germany. Most of Europe from the Iberian peninsula to Scandinavia was involved in the war at this point.
After a few successful attacks on France, the Empire began losing the war. Bernard of Saxe-Weimar and the Swedish generals Banér, Torstensson and Wrangel won important battles across Germany.
The war ended in 1648 with The Peace of Westphalia, where France and Sweden together with their German allies stood as victors.
I apologize for the many spelling errors in the first version of this write-up. I have corrected those I found so far and also corrected the fact about the outcome of the battle of Lützen.