Short answers, pulled from the story.
Resistance during World War II ranged from armed raids, assassinations, and uprisings to non-violent sabotage, strikes, espionage, underground press, document forgery, and hiding people to protect them from deportation. Resistance groups also ran escape lines for Allied military personnel caught behind Axis lines and gathered intelligence on German operations.
The Polish Home Army, known as the Armia Krajowa or AK, numbered around 400,000 fighters in late 1943, making it by several historians' accounts the largest resistance organization in Nazi-occupied Europe. Soviet partisan numbers and the Yugoslav Partisan numbers were comparable; the French Resistance counted an estimated 200,000 activists with a further 300,000 substantially involved.
Witold Pilecki was a Polish resistance member who in 1940 voluntarily allowed himself to be captured in a Warsaw street roundup and sent to Auschwitz concentration camp. Once inside, he organized an underground group called the ZOW and began transmitting reports about the camp and its genocide to the Polish Home Army. Beginning in March 1941, those reports were forwarded to the British government in London and became the first intelligence on the Holocaust to reach the Western Allies.
Operation Anthropoid took place on the 27th of May 1942, when Jan Kubiš and Jozef Gabčík, two Czechoslovak soldiers from the army in exile, attacked Reinhard Heydrich, the SS-Obergruppenführer and chief architect of the Final Solution, in Prague. Heydrich died of his wounds and became the highest-ranked Nazi assassinated during the war. The German reprisals killed over fifteen thousand Czechs and included the complete destruction of the towns of Lidice and Ležáky.
Norwegian saboteurs conducted a series of raids on the Vemork hydroelectric plant and its heavy water production. The campaign ended on the 20th of February 1944 when saboteurs bombed the ferry SF Hydro, which was transporting railway cars loaded with heavy water drums across Lake Tinn for shipment to Germany. Its sinking effectively ended Nazi nuclear ambitions, and the British SOE later called the full series of raids the most successful act of sabotage in all of World War II.
Żegota, formally the Council to Aid Jews, was a secret organization founded in September 1942 by Zofia Kossak-Szczucka and Wanda Krahelska-Filipowicz in occupied Poland, the only country in occupied Europe with such a dedicated organization. Over 50,000 Jews who survived the war received some form of help from Żegota. Its most well-known activist, Irena Sendler, smuggled 2,500 Jewish children out of the Warsaw Ghetto, provided false documents, and placed them in homes outside the ghetto.