This is my wheelhouse, but I'm in the middle of crunch time, so (probably fortunately for you), I'll keep it rather short. EDIT: This.. did not happen.

The war is best characterized by a series of phases, typically defined by shifting alliances and the "intervention" of new powers. The traditional narrative is that the TYW is a war between Protestants and Catholics centered in the Holy Roman Empire. While not untrue, this is also an oversimplifcation for a number of reasons. /u/Hazzardevil has already mentioned that Catholic France joined the "Protestant" cause, while Protestant Denmark sided with the Catholic/Imperial forces in the last years of the war.

The primary reason for the complexity is the degree of Habsburg preeminence in early modern Europe. At the commencement of the war in 1618, the Habsburgs ruled Spain and its empire (including the lower half of the Low Countries and the New World), Austria, Hungary, Bohemia (much of the modern day Czech Republic), and firmly held the title of Holy Roman Empire. Effectually, they were Europe's most powerful dynasty.

When the war initiated, the earliest Protestant leader (Frederick V, Count Palatine) explained the war as much about the constitutional matter of preserving "German freedoms", by which he meant noble rule, in the Holy Roman Empire, as a matter of protecting the practice of Protestantism. In fact, the two issues were inextricably aligned: the Habsburgs were predominant in the Holy Roman Empire, and were actively re-Catholicizing the nobility in their lands. The "Catholic" armies that supported the Habsburg cause are often called the "Imperial" army. Similarly, calling their opponents "Protestants" elides the difference between Lutherans and Calvinists, who disliked each other nearly as much as they hated Catholics.

So, essentially, the factions in the war were "nations who supported Protestantism, either sincerely or as a means with which to hurt the Habsburgs and personally gain" and "the Habsburgs and whichever powers felt that Habsburg hegemony favored them". The latter arrangement remains stable throughout the war, while the former group sees constant loss and expansion.

Broadly:

The first phase, the Bohemian Revolt I have already mentioned, was largely a regional affair. Pitted on one side were the nobilities of Austria, Hungary, and Bohemia, alongside the Palatinate and a collection of smaller Protestant principalities in the Empire; on the other side were Spain, Emperor Ferdinand and loyalists in Austria, and Protestant Saxony. The first side sought to protect their right to practice Protestantism openly and to support Count Palatine Frederick V's election to Bohemia, but were soundly defeated by the Emperor and his allies.

After his victory, Ferdinand aggressively forced Catholicism onto Bohemia, and the entire affair caused fear in Denmark, a Protestant state with significant interests in Protestant cities and principalities in the Northern Empire. King Christian IV of Denmark, collecting subsidies for the hiring of troops and provisions from England and France, now attacks the Imperial forces in 1625. Under the famous general Wallenstein, the Imperial forces press onto peninsular Denmark and ultimately force them from the war. The Imperial forces consolidate their victories in the Empire even further.

Next, the Swedes intervene in 1630, led by their dashing king, Gustavus Adolphus, who were also supported heavily by the French. The Swedes have very tremendous success early on, but King Gustav's death in 1632, rising costs, and a major defeat a couple of years later push back the Swedes—who, nevertheless, would continue fighting for the rest of the war. Again, the Imperial forces secure their position in the Empire.

Now, in 1635, the French are greatly concerned with the level of Habsburg success in the previous years of war, and decided to intervene directly themselves. Unlike the Danes and Swedes, the French are able to absorb military losses and conquests and continue fighting, and are able to put enough pressure on the Spanish arm of the Habsburg dynasty to weaken the Austrian arm in the Empire. Nevertheless, the war continues for another thirteen years, until, exhausted by decades of war, the Imperial forces and the French (who were facing severe unrest as the Fronde began) agree to reach a peace in 1648.

tl;dr Basically, a core pro-Habsburg, primarily Catholic force contended against almost every other major power in Europe, along with many of the Protestant princes of Germany, in waves over three decades of war.

Sources:

Brennan C. Pursell, The Winter King: Frederick V of the Palatinate and the Coming of the Thirty Years War.

Peter Wilson, Europe's Tragedy: The Thirty Years War.