In a sense, everything Hitler did post WW I was oriented toward another one. The 1939 invasion of Poland was just the final step. He infiltrated and became a member of the Nazi Party as an intelligence agent of the German Army, but obviously went his own way after that. He studied the revolutionary strategies of Lenin and improved upon them to seize power, and his economic policies (and his charming of the German industrial magnates) led to the most amazing economic recovery of the 20th century. But it was his political strategies aimed against the Western republics and the Soviet Union that brought on the war.
He struck at the root of Western power and prestige by the annexation of Austria, followed by Czechoslovakia. The anschluss was accomplished easily, through propaganda and intimidation. Being Austrian by birth and the leader of a resurgent Germany, many Austrians supported this. That what was left of Austria after Versailles was largely ethnically German aided him. His claim that he wanted to annex the part of Czechoslovakia called the Sudetanland to "protect" Germans living there who were oppressed by the Czechs may sound thin to us today, but this area had been part of Germany before the Versailles Treaty, as had much of Poland. His intimidation of Czech President Edvard Benes, a man in ill health and with no military chance of successful resistance, worked. Hitler annexed half of the country, and then the rest.
During this period he also supported the fascists under Franco in Spain during the civil war there, thus further chopping at the roots of Western power. Although Franco stayed neutral in the War and thus did not help Hitler, the loss of Spain and its territory on the mainland of Europe from the Western powers weakened them strategically.
The Western democracies played into his hands by the policy of appeasement, as he knew they would. When he wanted to annex Poland to "protect" the Germans there, Britain and France drew the line and promised to declare war. This was foolish, as they had no possible means of militarily aiding the Poles, thus handing Hitler a major victory both politically and militarily right at the outset of the war. He cut their support in Eastern Europe off and humiliated them at the same time, while protecting his eastern flank with the non-aggression pact with the USSR.
His manipulation of the personalities of other leaders was masterful, and he grasped a principle few military leaders do, that the key is to beat the enemy before the fighting actually begins. Unfortunately for him, Germany's economic and industrial might was simply not adequate in the end, although it was only by the cooperation of Churchill and Roosevelt before the war that the foundation of Hitler's downfall was laid.
Hitler purposefully laid bare his entire plan before the war in his book Mein Kampf, realizing that people tend to overlook what is right beneath their noses. The best explication of Hitler's strategy, sucesses and eventual failure is B. H. L. Hart's book Strategy, which I highly recommend.
If you are looking for a direct answer, Hitler invading Poland was the thing that started the war, although many of his previous actions can be considered the build up to war.