Prepare your mixing space to reduce noise sources not related to your recording. In particular, make sure that cables carrying power cross cables carrying audio signal, if they must cross them at all, at right angles, to minimize induced hum. Check all audio connectors for solid connections and replace any microphone cables that may be suspect.
Delete or mute the sections of each track in which there is no instrument or voice performance. Small amounts of noise can exist in quiet sections that, when added with other tracks, can become audible in aggregate. (Noise gates and automation can also take care of this duty automatically. See your software documentation for further information.)
Identify problem frequencies using a parametric equalizer. Use one notch filter at its narrowest Q setting, boosted to maximum. Sweep it back and forth across the frequency spectrum until the noise you wish to remove is highlighted. Reverse the boost to cut the frequency as much as possible without affecting desired musical content. Increase the width of the Q setting to capture a wider range of frequency. If the offending noise is in a narrow band, it can be reduced or eliminated using this method.
Minimize the use of further compression or boosted equalization on a track containing noise. Both will increase the level of the noise along with the level of performance, as well as adding small amounts of noise themselves.
Use a noise reduction plug-in if you have access to one. The plug-in will likely have a method to sample the noise during a quiet section, then remove the noise signature from the entire track. Avoid extreme settings to prevent unwanted effects on performance material.