A lot of the safety comes down to the insane amount of computers and maintenance. A commercial plane will almost never fly again after it lands without undergoing maintenance of some sort. There are dedicated teams of people in the flight control towers that monitor everything and tell a plane where and when to land. The reason why they're so safe is because the operations and flight of a single aircraft is not solely the responsibility of the pilots. There are dozens of people involved in making a flight safe that you will never even see. Also there are far fewer planes in the sky than cars on the road.

As for how they actually physically fly... I'm sure someone else can explain it better lol