I know how Superman flies.
His super strength allows him to force the cells in his body into any direction he wants to go. Similar to how leaning one way or another makes a person on a motorcycle turn left or right. Being Kryptonian, this forcing is massive in scale and momentum.
It’s not levitation or some other thing. It’s purely another physical attribute to being from Krypton and supercharged by our yellow sun.
Laser eyes, though? I have no theory on how this would work.
I read that, over the years they kept making Superman stronger and stronger (like laser vision instead of telescopic or x-ray vision) and to the point where he became invincible and there was no suspense to the stories anymore. The writers had to start making slowly weaker to compensate.
-PJ
Superman flies because Chuck Norris gave him permission to fly.