Short answers, pulled from the story.
Nasjonal Samling was founded by Vidkun Quisling, a former Norwegian Minister of Defence, along with a group of supporters including Johan Bernhard Hjort. The party was founded on the 13th of May 1933, though it chose to celebrate its founding on the 17th of May, Norway's national holiday.
During the German occupation, Nasjonal Samling supplied most of the ministers for the government assembled by Reichskommissar Josef Terboven. Quisling was named minister president on the 1st of February 1942. The party became the only legal party in Norway from 1942 to 1945, though real authority rested with Terboven, who answered only to Adolf Hitler.
Nasjonal Samling reached its peak membership of around 44,000 in November 1943. Membership had stood at roughly 2,000 when the war began and rose to 22,000 by December 1940 following the German invasion.
Nearly 50,000 people were brought to trial as collaborators after the war. Approximately half received prison sentences. Quisling was executed for treason, along with a few other prominent NS members and several German officials in Norway.
Nasjonal Samling never elected a single member to the Storting. Its best pre-war result was 2.5% of the vote, which it received in the 1933 parliamentary election.
Knut Hamsun, the Nobel Prize laureate, was a well-known sympathiser of Nasjonal Samling but never formally joined the party. After the war he was deemed mentally unfit to stand trial, and the question of his ties to the party was never resolved in a courtroom.