The noise gate is a traditional and very effective method of controlling unwanted noise in a signal. Normally when a signal is noisy, the component that you want - the voice or instrument - is louder than the noise. So the gate can be set so that it opens when the voice or instrument sounds, then closes when it stops, thus shutting off the noise.
This is a simple demonstration of a noise gate on a bass guitar recording that has quite a lot of amplifier noise.
The video is best watched full-screen, and you should listen on studio monitors or studio grade headphones.
Great home recording starts with a great home recording studio. It doesn't need to be expensive if you know how to select the right equipment for your needs.