Short answers, pulled from the story.
Admiral Rae Sloane and Commandant Brendol Hux became the de facto founders of what would become the First Order. They reorganized fugitive Imperial remnants into a hermit kingdom spending three decades instigating a cold war against the New Republic.
The First Order introduced as fictional military movement in 2015 film The Force Awakens created by J.J. Abrams. Official reorganization into name occurred about six years prior to film release according to Star Wars: Bloodline novel.
Fugitives reorganized themselves into a hermit kingdom spending three decades instigating a cold war against the New Republic. They secretly pushed into the Unknown Regions to seize new undeveloped worlds for resources.
The First Order lacks the galaxy-wide resources the old Empire once commanded. Their military adapted to a quality over quantity philosophy to make efficient use of few resources.
First Order stormtroopers are kidnapped from their home worlds and trained from birth. Soldiers undergo constant training in war games and simulations making them effective one-on-one against conscripts.