You can consider this post a complement to the post “Cleaning it up”which explains how you can deal with pops and clicks, as well as cutting out unwanted sounds from your recordings. While pops and clicks can be called “noise” in one sense, it’s not actually the kind of noise that we usually mean when we’re talking about noise in audio discussions.
For a technical description of noise in audio, see the Audio lingo post “Different colors of noise”.
If your recording is covered in noise, cutting usually won’t help much as the noise will likely still be underneath the voice (or whatever you’ve recorded). The EQ can get you a bit on the way, but usually you’ll want to use proper noise reduction software for this purpose. In the past I’ve posted about RX from iZotope, and even posted a short clip on what it’s capable of with little effort.
The way many noise reduction products works is that you simply highlight a short piece of the audio that is only noise (i.e. between the words) and tell it to analyze that and remove similar sounds. Depending on how advanced the product is you can do a whole lot of settings before removing it to make sure that you don’t remove parts of the sound that should be there.
There are of course a lot of noise reduction software (and hardware) out there other than RX, and I’ll try to cover them in another post in the near future. It’s even possible that your recording software already includes some sort of noise handler.