Background Noise Reduction in Audio signal
Depends a bit on the type of noise. If it's hum or buzz, you need to clean up your recording electronics and if push comes to shove you may be able to notch it out. 

Real acoustic background noise is difficult to remove. You may want to read up on "blind source separation". Here are a few examples http://cnl.salk.edu/~tewon/Blind/blind_audio.html