Some times as a video editor, you encounter really badly recorded audio, and all you have is Premiere to work with at your workstation.
This is what I use on Premiere Pro CC to make it slightly better.
Audio effects > Denoiser + Dynamics, Enable Auto Gate
Depending on how bad the audio is, sometimes just one filter is enough.
But yes, for audio recording it’s usually rubbish in rubbish out, and sometimes it is just an unfortunate accident.
Do leave a comment if you this works or if you have a better result!
Oct 2015 Edit: There’s an even better way to remove background noise if you have Adobe Audition. I will create a step by step instruction in another post.