On December 12, 2017, a bill was signed into law that requires UAS (drones) pilots in the United States to register their drones with the FAA. There has been some confusion as there was a rule previously that had been withdrawn.
A great place to start is to visit the FAA getting started with drones page.
The page for drone registration can be found here.
The page for pilots who wish to fly professionally, they'll want to visit this page. This license is generally referred to as Part 107.