Audacity includes many built-in effects and also lets you use plug-in effects (VST plug-ins) on the Macintosh and Windows formats.
To apply an effect, simply select part or all of the tracks you want to modify, and select the effect from the menu. Titles which end in an ellipsis (...) will bring up a dialog asking you for more parameters.
This is the most general type of filter. If you're careful, you can use it to highlight exactly the frequencies you want. However, doing an FFT filter is more likely to result in artifacts, especially if the filter you draw is not smooth.
Removing noise is a two-step process. In the first step, you select a portion of your sound which contains all noise and no signal, in other words, select the part that's silent except for the noise. Then choose Noise Removal... from the Effect menu and click Get Profile. Audacity learns from this selection what the noise sounds like, so it knows what to filter out later.
Then, select all of the audio where you want the noise removed from and choose Noise Removal... again. This time, click the "Remove Noise" button. It may take a few seconds or longer depending on how much you selected.
If too much or not enough noise was removed, you can Undo (from the Edit menu) and try Noise Removal... again with a different noise removal level. You don't have to get a new noise profile again if you think the first one was fine.
Removing noise usually results in some distortion. This is normal and there's virtually nothing you can do about it. When there's only a little bit of noise, and the signal (i.e. the voice or the music or whatever) is much louder than the noise, this effect works well and there's very little audible distortion. But when the noise is very loud, when the noise is variable, or when the signal is not much louder than the noise, then the result is often too distorted.
Future versions of Audacity may include improved versions of this effect.