Most home recording takes are going to have a little bit of background noise, no matter how careful we are to record really clean. 

Noise removal/reduction can help.  But it does have some limits. 

a.) It only works *really* well on steady noise, like a fan somewhere in the background (computer fan, for example), or "AC hum".

b.) It can sometimes make your instrument or voice sound a bit weird, or can actually make noises that weren't there in the first place.  Those are called "artifacts" or sometimes are nicknamed "pixie dust", since they sometimes will sound like a high pitched random trilling noise that sort of comes and goes.

c.) It can only work well if you have a reasonable length sample of the noise that was present when the recording was being made that is *just* the noise, without you playing or even moving around. 

Even with those considerations, though, it is still quite useful, and not hard to do with Audacity.  First, let's look at a track with some noise.

The big blobs are showing where I said "test 1, 2, 3, test 1, 2, 3".  The thick line that goes all the way through the recording is noise.  Quite a lot of noise, actually.  Two window fans and my computer's cooling fan whining away on "high" setting.

So here's how we fix it.. First we click and drag to highlight several seconds of the part that we know is just noise.

Next we go to Effects>Noise removal.  I'm not sure as the menus are the same in the windows and mac versions of Audacity, but it is one of the default plugins included with Audacity, so you'll find it wherever Audacity has your effects. 

And we'll get a pop-up box that looks like this..

For this step we tell it to "Get Noise Profile".  That will usually only take a second or two.  Now we want to deselect the bit we highlighted for the noise profile sample, or Audacity would think we only want it to work on the highlit part. I usually do that by just hitting the "Skip to start" button, which is the 4th round button from the left near the top of the Audacity screen.

Then we open noise removal again, to get back to the same popup box, and tell it "OK", and it will do the removal.  That can take anywhere from a couple of seconds to a minute or two, depending on your computer and how long the recording is.  When it is done, we should have something that looks like this:

Yay!  See how the thick line is all gone now?  Congrats, you have just done "noise redux".

But always check your work.  When doing this on your own music tracks, listen the track through all the way to make sure everything sounds ok.  Most of the time it will.

On the occasions where it doesn't and it sounds weird or has odd clicks or "pixie dust" or whatever, use the Edit-Undo to go back to before you selected the section for the noise analysis sample.  Highlight a slightly different section (it can be mostly the same, just try to start and end it in slightly different spots) and go through the process as before and that will *usually* fix it.

If it doesn't well, you could try tweaking the noise removal settings.  But when you are recording yourself, it is pretty easy to just do another take and try to eliminate the background noise better from the room this time.  It is very easy to end up spending more time tinkering with settings than you would by just re-doing the recording.  LOL