Hi, I'm a student of German and politics rather than history directly. I can't provide a hyper detailed account of Wilhelm II's role in the First World War but what I can do is give some background to the constitution of the German empire - especially how it relates to the Kaiser - and some of the background leading up to in the Bismarck period (as constitutions and Bismarck are some of my areas of interest).

the constitution: the constitution of the German Empire was a lot like the constitution of the later Weimar Republic (for those of you aware of it) except with far fewer rights.

There are three important actors in the constitution for our purposes here. The Kaiser, the Chancellor/Prussian first minister, and the Reichstag (parliament). Unlike in other Western European states of this time, the hereditary Kaiser was arguably the most important individual in government. This is because he had the power to appoint (and remove) the chancellor, who was effectively head of government. The parliament's consent was needed in order to pass legislation and budgets, but the parliament could not dismiss the chancellor and so didn't necessarily have the ability to intervene in day to day governance.

During the early period of the German Empire whilst Wilhelm I was Kaiser the Kaiser typically left most affairs of state to the first minister. The Kaiser would simply set out broad objectives. In accordance with this Wilhelm I appointed Bismarck chancellor who is one of Germany's most effective leaders ever. Bismarck stayed on this job for decades and drove his own policy agenda.

After Wilhelm I died - and 100 days later the crown prince also died - Wilhelm II took the throne. Wilhelm II was a very involved Kaiser. He had personal disagreements with Bismarck and so dismissed him as chancellor after decades of service shortly after acceding the throne. Wilhelm II made a string of foreign policy announcements which have been considered by diplomatic historians as wild and inconsistent - even getting the name 'zigzag diplomacy'. This included trying to court Britain to join their bloc in the upcoming war whilst also announcing road building projects and colonial ambitions that threatened British colonial interests.

As for the war itself I am no expert so can't speak on that. But given that the German constitution afforded Wilhelm II huge political and legal powers and influences, and given the character of Wilhelm II as an involved monarch it likely he continued playing an important role. And as for the lead up to the war Wilhelm II is more responsible than any other individual, maybe even more so than the assassins in Sarejavo.

Sources

Preusens Könige: ein Leben zwischen Hoffnung und Revolution ( Heinz Ohff)

Bismarck, (Korb)

Various trips to the Deutsches Historisches Musuem

During the war, Wilhelm's authority varied.

At the start he was the supreme commander of the German armies and was very involved (not in decision making, but in looking at the results) of "his" armies. He watched their progress jubillantly, was angered when they lost, and pleased when they won.

As the war dragged on, cracks began to form, starting with the military high command. To explain this, let's start with the war itself.

World War I for Germany was divided in two: the Western Front, comprising France, German Elsaß-Lothringen (Alsace-Lorraine), Luxembourg, and Belgium; and the Eastern Front, a huge space split into Germany's sector, Ostpreußen (East Prussia), Silesia, and Russian Poland, and Austria-Hungary's southern sector, primarily focused around Galicia (Austrian Poland/Ukraine) and the Carpathian Mountains.

The Schlieffen Plan was developed by Germany to counter this was, and was Germany's only war plan: it was created by Chief of of the Imperial General Staff Field Marshal Alfred von Schlieffen, and taken up and refined by his replacement Moltke the Younger. It was Germany's only plan as both field marshals saw it as the only way Germany could succeed, and a new plan in this era took literally years and hundreds of staff to complete: it was essentially a stack of papers detailing train times and cargoes, orders for generals and their officers, and the use of roads by X for Y time.

The Schlieffen Plan necessitated Germany destroying France in 4-6 weeks so Germany could focus all of its might on Russia, presumed to be the stronger (and definitely more numerous) power. The hope was that France would be crushed and Paris taken in a short span of time, the French routed as quickly and efficiently as they were in the Franco-Prussian War that created the German Empire.

Kaiser Wilhelm was absolute sovereign of his empire and an involved man in the running of his country, but he could not stop his country's entry into the Great War for two reasons: 1) because Russia mobilized first, and 2) because if Germany mobilized, it had to use the Schlieffen plan; there were no alternatives. In this sense, he had little power, but at the beginning of the war it was still he - at the insistence of his generals - that ordered German mobilization.

Going back to the point of it being a two front war, German High Command, and Kaiser Wilhelm, were based on the Western Front once the Schlieffen Plan ground to a halt. But in Liege, the great Flemish fortress-city, a man made himself renowned by practically single-handedly capturing what was regarded as one of the greatest fortress complexes in all of Europe: Erich von Ludendorcf.

Ludendorff was regarded as a hero and personally awarded a medal by the kaiser, and shipped off to East Prussia when it was learned two Russian armies invaded far sooner than expected. Paul von Hindenburg was made commander and Ludendorff his chief of staff, and they were to protect East Prussia, traditional homeland of the Junkers elite (Prussia's military class) from the Russian incursion.

On the western front, Moltke was replaced with Field Marshal Erich von Falkenhayn; this was a momentous event, and Ludendorff would later say "I can only love or hate, and I hate Falkenhayn."

As the Western meatgrinder intensified, the outnumbered Germans in East Prussia discovered that the Russian armies had split up and were too far away to support each other. Ludendorff and Hindenburg completely encircled and destroyed the first in the Battle of Tannenburg, for which they attained enormous prestige and respect of their prowess, and then nearly did the exact same thing to the second at the Battle of the Masurian Lakes.

This was the beginning of the end for Wilhelm. Despite their victories, Ludendorff - a worriable man - knew that the Russians had superior numbers and feared they could overrun Germany. In the West, the Battle of the Marne that had caused Moltke's downfall had sapped German strength, and so Falkenhayn felt he could not send troops east. When Ludendorff demanded them, Falkenhayn sent less than he liked - and so the animosity began.

Ludendorff saw their victories over the undersupplied Russian armies and repeatedly requested more troops and the ability to go on the offensive, trapping or destroying Russia's Polish armies and ending the enemy's offensive power; German High Command rebuffed him repeatedly.

During this time, Hindenburg pretty much stopped being a general, and let Ludendorff do most of the military work: he slept, ate, and lazed around, visiting planning rooms rarely.

Ludendorff, the Hero of Liege and Tannenberg, presided over further victories over the Russians. Wilhelm grew increasingly dissatisfied with Falkenhayn, who met his end after the disastrous and pointless bloodbath that was Verdun and the British assaults at the Somme. Wilhelm made Ludendorff "Quartermaster General" and Hindenburg de jure chief, but in reality Ludendorff was the leader.

This is when Wilhelm's power began to slip. The kaiser was never a terribly strong-willed man, and Ludendorff was pretty much unstoppable due to his achievements. He gained more and more powers, as Quartermaster General grabbing more ways to run the war effort by slowly running the government as well as the military to an almost obsessive degree.

The climax in Ludendorff's rise to power (imo) came when he and the military lobbied for unrestricted submarine warfare; the kaiser was reluctant/opposed and was supported by his chancellor. Ludendorff demanded, and got, the submarine warfare allowed, and then threatened to resign unless his chancellor was sacked; Wilhelm relented, and so was no longer Germany's head of state.

From this point on (earlyish 1917) Ludendorff was Germany's military dictator in all but name, controlling all levels of the German state. He even slowly took over Austria's military decisions as the Hapsburg regime crumbled and grew to be nothing more than a weak puppet of Germany's. His resignation days before the war formally ended can be said as marking the end of the German Empire.

On Hindenburg, he held very little, and was less than interested in, running Germany; even as Chancellor of Germany during Hitler's rise he had a distaste for the man and was nominally a monarchist, being from the old Junkers elite. Nonetheless, he still didn't stop Hitler, and his only truly notable action during the war was his leadership during Tannenburg.

Source: G. J. Meyer's A World Undone