Short answers, pulled from the story.
The League of Nations was the first worldwide intergovernmental organisation whose principal mission was to maintain world peace. It was founded on the 10th of January 1920 by the Paris Peace Conference that ended the First World War.
The United States never joined the League of Nations because the Senate failed to ratify the treaty, voting 49-35 on the 19th of March 1920, short of the required two-thirds majority. Senate Republicans led by Henry Cabot Lodge wanted a reservation that only Congress could take the country into war, and Woodrow Wilson refused to compromise.
The League of Nations was headquartered in Geneva, Switzerland, after moving from London on the 1st of November 1920. Its first permanent home was the Palais Wilson on Geneva's western lakeshore, named after Woodrow Wilson.
The League of Nations consisted of 42 founding members in November 1920 and reached its largest extent of 58 member states after the Soviet Union joined on the 18th of September 1934.
The League of Nations failed because it lacked its own armed force and depended on the great powers to enforce its resolutions, which they were often reluctant to do. It proved incapable of preventing aggression by the Axis powers in the 1930s, and the onset of the Second World War in 1939 showed it had failed its primary purpose.
The League of Nations strengthened collective security, gave a voice to smaller nations, and fostered economic stability in Central Europe in the 1920s. It created the Nansen passport for stateless refugees, helped 425,000 ex-prisoners of war return home, and pressured nations such as Afghanistan, Iraq, and Nepal to abolish slavery.
The League of Nations ceased operations on the 18th of April 1946, when many of its components were relocated into the new United Nations. Three of its institutions carried forward: the International Labour Organization, the Permanent Court of International Justice as the International Court of Justice, and the Health Organisation as the World Health Organization.