Short answers, pulled from the story.
General Leia Organa and several other Rebel veterans formed the Resistance as a check on the designs of the First Order. The group recruited from both the New Republic military and worlds that experienced the worst of the Empire.
The Resistance appeared one year after the Battle of Endor when General Leia Organa broke away from the military to form the group. They established their base on the jungle moon of Ajan Kloss one year after The Last Jedi.
The Resistance established its base on the jungle moon of Ajan Kloss during The Rise of Skywalker set one year after The Last Jedi. They traveled to Exegol with their fleet to face the Final Order before emerging victorious.
General Leia Organa and several other Rebel veterans broke away from the military because the heavily demilitarized New Republic did not view the First Order as a true threat. They formed the Resistance as a check on the designs of the First Order while the Senate secretly funded and armed the group.
Command transitions occurred between key figures including Leia Organa, Poe Dameron, and Vice Admiral Holdo during moments of extreme danger or loss of leadership. Vice Admiral Amilyn Holdo assumed temporary leadership when Organa was seriously wounded and later commanded the fleet when Admiral Ackbar was killed and Leia entered a coma.