I looked through the FAQ and search function and was very surprised that I couldn't find this question before. If I simply missed it could someone please direct me to the appropriate thread?
In general, taking on the largest empire in the world (Britain), the largest economy in the world (the United States) and the largest army in the world (the Soviet Union) is not a particularly good strategy. Germany achieved many successes during the early bits of the war (Poland, Belgium, France, Netherlands, Denmark, etc), of course, achieving near-total domination of the European continent before the decided to declare war on the Soviets. However, the Germany economy was severely overstretched and incapable of producing war materials as efficiently as the British (contrary to popular belief, German manufacturing during the war was supremely inefficient, especially before 1942), let alone the United States, who was supplying the British even before they entered the war. The Luftwaffe was unable to take Britain out of the war and the aerial Battle of Britain in 1940 really only served to embolden the British, and the U-Boats of the Kriegsmarine, whilst very succesful, weren't able to starve the British Isles despite their attempt to do such. Germany's invasion of the Soviet Union in 1941 was very succesful at first but it was not able to knock the Soviet Union out of the war, and with when the US was brought into the war in December 1941 any hope of victory for the Germans pretty much was over. The Soviets would just not roll over (unlike what the Germans and many foreign observers predicted) and war on the Eastern front was very costly in terms of men and materials, and the allies, thanks to population and industrial capacity (US supplies were very important to both the British and Soviets), could more easily replenish and increase their armed forces than the Germans could. Germany was undoubtably a strong state, but it was simply nowhere near capable of taking on multiple superpowers at once. By early 1943 Germany was being pushed back in both the East (where they lost an entire army at Stalingrad) and in North Africa - the overly ambitious drive into the Middle East failed with Rommel's defeat at El Alamein in Egypt in 1942, and the British and soon Americans began to squeeze the Axis out of the entire region from both sides after invading Vichy France's colonies in western North Africa. By mid-to-late 1943 the Allies had invaded Italy and Germany was on the defense in the East, and from 44 onwards Germany would loose huge amounts of men in the East as the Allies opened up a new front in the West with the D-Day Landings. From then on they were fighting on two fronts at once, and the war was clearly lost.
TL;DR: they took on too many powers at once, and were not nearly capable of sustaining their overly-ambitious war effort.