Answer:
Czechoslovakia and Austria were taken over by Germany before the fighting started.
Germany got involved by invading Poland (1939).
Poland (1939), Denmark, Norway, France, Belgium, Netherlands, Luxembourg (all invaded in 1940), Yugoslavia (1941) and the Soviet Union (1941) by being invaded by Germany.
The Soviet Union didn't have clean hands, however, having participated in the 1939 invasion of Poland and subsequently subverting Estonia, Latvia, and Lithuania.
Great Britain joined in when Poland was invaded, engaging in naval combat and fighting in defense of France. All members of the British Commonwealth, like Canada, Australia, New Zealand, India and South Africa supported Britain, also the African colonies, such as the Gold Coast (now Ghana).
Italy invaded Albania (1939) and Greece (1940), which was also invaded by Germany (1941). In 1940 Italy attacked France, which led Britain to declare war on Italy.
Finland was invaded by the Soviet Union, then kept it going after Germany invaded the Soviet Union.
Rumania and Hungary were co-opted by Germany and joined in the Soviet invasion.
Spain more-or-less stayed out, although there were a few Spanish troops as part of the Axis forces on the Russian front.
The United States had war declared by Germany after the United States declared war on Japan after the Pearl Harbor attack, although US ships had been battling German ships for some time while participating in support of Great Britain.
Mexico and the Central American countries joined up some time after Pearl Harbor.
Brazil and maybe some others in South America did, too.
Japan invaded China first in 1931, then on a much bigger scale in 1937, in 1941 the Philippines (a US territory at the time), the Dutch East Indies (now Indonesia), French Indochina, and the British colonies Malaysia, Singapore and Burma. They got some miles into India, but were thrown back.