I understand how Geordi's visor works in universe, but what about out of universe? How does Levar Burton see with that contraption covering his eyes?
It's a grid. You can see through the gaps.
And if you scroll along to 1:40 in this "making of" video from StarTrek.com, you can see what the view is like from the inside:
That being said, Levar Burton said it wasn't easy:
AVC: Even with the visor being hard to see through?
LB: Yes, the visor was really hard to see through, but guess what? It made me a better actor. Trying to communicate with people without them being able to see your eyes is not easy, I learned.
The VISOR (Visual Instrument and Sensory Organ Replacement) was actually modeled after a hair barrette. I remember hearing one person say it was actually molded directly from a barrette and slightly modified.
It's not solid, it has vertical bars that Levar Burton could see through: