Above all else, I think it is critical to note that Hitler was more than willing to sacrifice secondary or tertiary ideological goals in order to achieve his primary ones. The very fact that the Night of the Long Knives and the Molotov-Ribbentrop Pact occurred is clear evidence of this.
Hitler had long espoused rhetoric against the Soviet Union and the Jewish people, utilizing the fear of the so-called "Asiatic Hordes" that will sweep from Russia into "civilized Europe." However, Hitler also recognized that to destroy "Judeo-Bolshevist" Russia, he would need allies that flanked the Soviet Union. It was only natural that he looked to East Asia as a source of potential allies to keep the Soviets busy.
At this time, there were two major powers that fulfilled Hitler's objectives of posing a threat to the Soviets: Chiang Kai-Shek's Republic of China (Nationalist China/Kuomintang) and the Greater Japanese Empire (Dai Nippon Teikoku). Both of these countries not only feared and resented the Soviets (Chiang was fighting the Chinese communists, whom were supported by the Soviets to an extent, and the Japanese deeply feared a Soviet incursion into Japanese-held Korea and Manchuria) but also were in a position to be a military threat to them. However, they both had advantages and disadvantages: Japan was far more industrialized and militarized than China was in the short-term, but China already benefited from a substantial German industrial and military mission that had been established by the Weimar Republic's Reichswehr (later Wehrmacht) in an effort to conduct foreign policy independent of the civil government.
These factors, combined with a certain Asian mystique feeding into some of the more occult portions of Nazi ideology (the ever popular SS-supported expedition into Tibet being one example), caused the Germans to pursue a relationship with both the Chinese and the Japanese. They wanted to support the Chinese because of the large amount of natural resources that China had available to sell to the Germans (including rare materials like tungsten (or wolfram)). At the same time, the Germans took advantage of Japanese fears of Communism and attempted to get Japan to enter an alliance with Germany against the Soviets. There was a bit of a sticking point, however: the Germans also tried to bring the Chinese into what became the Anti-Comintern Pact, but the resulting drama caused by the territorial dispute between China and Japan over Manchuria and other parts of China resulted in the treaty being more or less neutered, and without China.
Things came to a head when Japan and China went to war in the Second Sino-Japanese War. At this point, despite German efforts to keep both of their Asian partners happy, there was Japanese pressure on the Germans to withdraw their military mission, especially after German-trained Chinese troops inflicted heavy casualties on Japanese forces. Tensions raised by things like Nazi Party member John Rabe drawing attention to the Nanking massacre did not help. While the Wehrmacht favored continuing to support the Chinese, Hitler and the Nazis (esp. Ribbentrop) decided to listen to the Japanese, reasoning that since war with the Soviets was coming sooner rather than later, the Japanese, being a more modernized military, would be a better ally against the Soviets. Still, there were still limited connections between the Wehrmacht and the Chinese as late as 1940 to revive the Sino-German cooperation.
In the end, the Japanese did little to satisfy Hitler's desire for an eastern ally. While certainly the Soviets were forced to keep a large amount of troops in the Far East to defend against a potential Japanese attack, the Japanese, after getting their noses bloodied against the Soviets at Nomohan, pursued a course of expanding south rather than north instead. The Germans managed to send the Japanese some intelligence on the weakness of the British and Dutch colonies' defenses, and there was pressure from the Germans to get the Japanese to attack Singapore. As they did in 1941, along with Pearl Harbor and other Pacific territories.
As the end of the Third Reich grew near, Hitler, in his Poltiical Testiment, wrote the quote that many people have mentioned below:
Pride in one's own race - and that does not imply contempt for other races - is also a normal and healthy sentiment. I have never regarded the Chinese or the Japanese as being inferior to ourselves. They belong to ancient civilizations, and I admit freely that their past history is superior to our own. They have the right to be proud of their past, just as we have the right to be proud of the civilization to which we belong. Indeed, I believe the more steadfast the Chinese and the Japanese remain in their pride of race, the easier I shall find it to get on with them.
What is important to note here is that this is extremely contradictory with certain other elements of Hitler's policies. Hitler had decreed that all Japanese were "honorary Aryans" yet here he says that the Japanese are superior to the German "Aryans." Why would a so-called "superior" people be placated by being being honorary members of an "inferior" race? Evidently there is a bit of a contradiction here, which can best be summarized as Hitler freely saying or doing things if he thought they would improve his chances of success in reaching his ideological goals: namely, the destruction of the Jewish people, the destruction of communism, Russia and "Slavdom" in general, and the creation of an eternal German Reich with all the Lebenstraum it would ever need.
Sources:
Yue Lan, General von Seeckt and Sino-German Cooperation.
Ian Nish, Japanese Interwar Foreign Policy
Please see the FAQ for answers, this question has been answered a number of times already. The following link has an overview:
I'm curious what the Nazis thought of Iranians... that is, the actual Aryans. Did they have any special place in the Nazi racial theory?