Why and how and to what extent was the First World War a global war?

WWI was a global war in the sense that every inhabited continent had troops who participated in the conflict.  British, French, and German colonial subjects all fought in the war, many of whom were drafted to serve in European trenches.  There were a few battles in East Africa and in the Pacific islands--Japan used WWI as an excuse to take over German-held colonies.  The Atlantic Ocean and Mediterranean Sea became battle zones, as German U-boats waged war against Allied shipping.  Manufactured goods and foodstuffs came from the Americas in order to fuel the Allied war effort.  The Middle East erupted into conflict as Britain and Germany both tried to control Muslims in the area to either fight against Allied areas or to overthrow the Ottoman Empire--ultimately, British efforts in the region were successful in forcing the Ottoman Empire out of the war.  The conflict was even taken to the United States in the form of German spies and saboteurs; German agents managed to destroy the Black Tom munitions plant at Jersey City.  

The end of the war was also an international affair.  British and French colonies wanted their own independence through Wilson's promise of self-government for all people, but were turned down.  The interwar period was important for nationalist movements in the Middle East, Asia, and Africa.  WWI also changed Europe as well, with the formation of Poland and the Baltic countries from land taken from the Soviet Union and Germany.  The Austro-Hungarian Empire split and the Versailles treaty makers created the nation of Yugoslavia in order to placate the nationalist movements there which started the war.