My LG Neon is about a month old with no damage. However, when I use the camera, the screen turns black and i can't take any pictures. I tried turning my phone off then on, but nothing works. How do I get the camera walking again?

This could happen due to the faulty camera or due to the software is not recognizing the hardware(camera).
Two solutions,
1. check if any software/hardware updates outstanding. u can do this by connectiong ur phone with ur PC suit. if any available , download it and see if the camera starts working. 2. Since it is not too old it has a live active warranty and in that case take it back to LG tech and get it fixed.