Important events in Europe
Arguably, the most important event in Europe in 1939 was when Nazi Germany invaded Poland. This invasion directly violated a previous deal made by Germany, Great Britain, and France. As a result of this, Great Britain and France declared war on Germany in September of 1939.
Besides that invasion of Poland, the Soviet Union and Germany signed a non-aggression pact in 1939 as well. This was important for the time being, as it prevented Germany from having to fight a two front war.
Important events in the United States
The US passed the Neutrality Act of 1939. The goal in passing this law was to avoid being dragged into a foreign war. This law stopped America from trading arms with countries that were involved in a war.