Since signing essentially a defensive pact against communism (i.e. the Soviet Union) in the mid 1930s, they had been slowly improving their relations. By the time the war started, Germany and Japan also started to recognize that they were going to need mutual assistance with critical supplies to keep a war machine moving. In 1940, they along with Italy signed a defensive pact called the Tripartite Pact that formally created what became to be the Axis Powers. Other smaller nations would join later, but Japan and Germany were the two main world powers that were involved.

The pact was essentially designed for intervention in a defensive war against the United States, although they were not explicitly mentioned in the treaty. Japan alleged that the United States' embargo of oil, rubber, and other war machine materials had been the first act of war between the two countries, which would make the U.S. the aggressor. Germany also envisioned conquering their slice of the world and wanted the United States to be a part of that.

This was coupled with the Nazi belief that the Americans, while being able to field a large army, would not be able to match anywhere near the quality of German soldiers, engineering, or technology, and they would be able to defeat the United States (or at least stalemate them).

Not to mention, the United States, while formally neutral, by December 1941 was nowhere near de facto neutral. They had already been providing materiel (essentially at no cost) to the British under the first Lend-Lease bill to Great Britain and China. Once war was declared, U-boats could begin to sink the American cargo ships and destroyers, not just their British escorts.

So in summary, Germany and Japan:

1. had mutual enemies including the United States and the Soviet Union,

2. was already de facto at war with the United States economy,

3. had a defensive treaty with Japan,

4. wanted to subjugate the United States, and

5. thought the United States would not have been able to effectively slow their conquest.