Depending on what you film and where you film it, you might not always have control of the sound and in particular, the ability to keep background noise to a minimum. If you have a video with background noise that you need to reduce, this excellent video tutorial will show you how to do it in Premiere Pro.
Coming to you from Josh Olufemii, this awesome video tutorial will show you how to reduce the background noise in your videos using Premiere Pro. The important thing to remember is that just like post-processing still images, it is always better to start with good data than it is to try to manufacture it in post. If you can get quality audio from the start, you will have a much easier time working with it in post (and you will have less work to do). Certainly, you can't always control the environment in which you will be filming, but doing things like using lavalier mics for interview subjects or picking a relatively acoustically isolated location can go quite a long way. If you need to do some additional cleanup after that, though, Premiere and Audition have some powerful tools. Check out the video above for the full rundown.