The main flying effect done for Superman is this weird whip pan effect, where Superman is crudely composited in front of brief snatches of quickly moving stock footage.
When hanging the actual actors on wires is too difficult, dolls will suffice.
Of course, you can just choose not to show Superman at all, as in this footage of Superman rescuing a plane.
A shot of Superman on the ground, obviously having just carried the plane to safety, completes the effect.
Another doll with an awesomely detailed bridge minature.
Superman can lift people by simply reversing the footage.
