Read this article on the origins of World War II. It provides a global perspective on the multiple causes and how each of the powers involved entered the conflict.
Declarations of war
Invasion of Poland

Grave of German soldiers fallen during invasion of Poland in Końskie. Visible inscription "For Fuhrer und Vaterland"
Between
1919 and 1939, Poland had pursued a policy of balancing between the
Soviet Union and Nazi Germany and agreed to non-aggression pacts with
both. In early 1939, Germany demanded for Poland to join the
Anti-Comintern Pact as a satellite state of Germany. Poland, fearing
a loss of independence, refused. Hitler admitted to his generals on 23
May 1939 that his reason for invading Poland was not Danzig: "Danzig is
not the issue at stake. It is a matter of extending our living space in
the East..".. To deter Hitler, Britain and France announced that an
invasion would mean war and tried to convince the Soviet Union to join
in this deterrence. The Soviets, however, gained control of the Baltic
states and part of Poland by allying with Germany by the secret
Molotov–Ribbentrop Pact in August 1939. London's attempt at deterrence
failed, but Hitler did not expect a wider war. Germany invaded Poland on
September 1, 1939, and rejected the British and French demands for it
to withdraw, which resulted in both to declare war on September 3, 1939,
in accordance with the defence treaties with Poland that they had
signed and publicly announced. However neither France nor
Britain provided significant military aid to Poland except small
operation known as Saar offensive. As of 1 September 1939 Poland was
only partially mobilized, which was largely the result of pressure from
the British and French ambassadors on the Polish government, fearing a
repeat of the mobilization scenario of war from 1914. The Wehrmacht also
had advantage in terms of the number of tanks and planes and the
technical advancement of its equipment.
On September 17, 1939,
the Red Army entered Poland from the east, and the Polish Command
decided to abandon the defense of the so-called Romanian Bridgehead and
evacuate of all its forces to neighboring countries. The last larger
unit of Polish troops capitulated on October 6, 1939, near Kock, but
some units went straight to partisan combat. Until the spring of 1940,
the resistance of irregular units in the region of the Świętokrzyskie
Mountains in central Poland lasted, but the struggle of these units
resulted in enormous repressions against the civilian population of the
region in which they operated.
Invasion of Soviet Union
Germany attacked the Soviet Union in June 1941. Hitler believed that the Soviet Union could be defeated in a fast and relentless assault that capitalised on the Soviets' ill-prepared state and hoped that success there would bring Britain to the negotiation table, which would end the war altogether.
Attacks on Pearl Harbor, the Philippines, British Malaya, Singapore and Hong Kong
The US government and general public in general had been supportive of China, condemned European colonialist policies and Japan and promoted the so-called Open Door Policy. Many Americans viewed the Japanese as an aggressive and/or inferior race. The Nationalist government of Chiang Kai-shek held friendly relations with the US, which opposed Japan's invasion of China in 1937 and considered it a violation of international law and of the sovereignty of the Republic of China. The US offered the Nationalist government diplomatic, economic and military assistance during its war against Japan. Diplomatic friction between the United States and Japan manifested itself in events like the Panay incident in 1937 and the Allison incident in 1938.
Japanese troops entering Saigon
Reacting
to Japanese pressure on French authorities of French Indochina to stop
trade with China, the US began restricting trade with Japan in July
1940. The end of all oil shipments in 1941 was decisive since the
Americans, British and Dutch provided almost all of Japan's oil. In
September 1940, the Japanese invaded Vichy French Indochina and occupied
Tonkin to prevent China from importing arms and fuel through French
Indochina along the Sino-Vietnamese Railway from the port of Haiphong
through Hanoi to Kunming, in Yunnan. The US decided that the
Japanese had now gone too far and decided to force a rollback of its
gains. In 1940 and 1941, the Americans and the Chinese decided to
organise a volunteer squadron of American planes and pilots to attack
the Japanese from Chinese bases. Known as the Flying Tigers, the unit
was commanded by Claire Lee Chennault. Its first combat came two weeks
after the attack on Pearl Harbor.
Taking advantage of the
situation, Thailand launched the Franco-Thai War in October 1940. Japan
stepped in as a mediator in the war in May 1941 and allowed its ally to
occupy the bordering provinces in Cambodia and Laos. In July 1941, as
Operation Barbarossa had effectively neutralised the Soviet threat, the
faction of the Japanese military junta supporting the "Southern
Strategy" pushed through the occupation of the rest of French Indochina.
The
US reacted by seeking to bring the Japanese war effort to a complete
halt by imposing a full embargo on all trade between the United States
to Japan on August 18, 1941, and demanding a Japanese withdrawal of all
troops from China and Indochina. Japan was dependent on the United
States for 80% of its oil, which resulted in an economic and military
crisis for Japan since it could not continue the war effort against
China without access to petroleum and oil products.
Attack on Pearl Harbor, December 1941
On
7 December 1941, without a declaration of war, the Imperial
Japanese Navy attacked Pearl Harbor with the aim of destroying the main
American battle fleet at anchor. Meanwhile, other Japanese forces
attacked the American-held Philippines and the British Empire in Malaya,
Singapore, and Hong Kong. The following day, an official Japanese
declaration of war on the United States and the British Empire was
printed on the front page of all Japanese newspapers' evening
editions. International time differences caused the announcement to
take place between midnight and 3 a.m. on 8 December in North America
and at about 8 a.m. on 8 December in the United Kingdom.
Canada
declared war on Japan on the evening of 7 December, and a royal
proclamation affirmed the declaration the next day. The British
declared war on Japan on the morning of 8 December and specifically
identified the attacks on Malaya, Singapore and Hong Kong as the cause
but omitted any mention of Pearl Harbor. The United States declared
war upon Japan on the afternoon of 8 December, nine hours after the
United Kingdom, and identified only "unprovoked acts of war against the
Government and the people of the United States of America" as the
cause.
Four days later, the US was brought into the European
war when on December 11, 1941, Nazi Germany and Fascist Italy declared
war on the United States. Hitler chose to declare that the Tripartite
Pact required Germany to follow Japan's declaration of war although
American destroyers escorting convoys and German U-boats had been de
facto at war in the Battle of the Atlantic. The declaration of war
effectively ended US isolationist sentiment, and the country immediately
reciprocated and so formally entered the war in Europe.