NID stands for network Interface device. In modern installations, it's a gray box mounted on the outside of your house that opens up to reveal the wires from inside and the outside cable. Its usually near where the electric comes into your house, but if the structure is older, it may not be there. Back in the day when there was no ILEC CLEC's and internet, the telco was the only source and they just put the protectors in the basement.
When you find the box, open it. It usually has a screw holding the lid closed, that's what the screwdriver is for. When you open it, there is a modular jack and plug arrangement that will disconnect the inside wiring from the phone company, usually a plug on a clip arrangement. Plug a regular phone directly into the jack that is exposed and listen for the buzzing. If it's still there, it's the phone company's problem, if it goes away, it's your trouble.
Buzzing/humming usually is outside. If it's inside, water or dirty jacks with foreign objects (spiders, etc) would cause it. You could also have some physical damage, but I'm guessing the buzzing is coming from outside.