You can quiet a noisy refrigerator by identifying the source of the noise and alleviating the issue. The cause of the noise may be mechanical, external or internal.
Check the back of the fridge. Noise emanating from this area often originates at the defrost timer, the condenser fan or the compressor. Clean the condenser fan blades, replace the compressor and replace the defrost timer to reduce the noise.
If noise is coming from the bottom, it may be caused by the drain pan. Securing the drain pan back into place is a straightforward fix of the issue.
Check inside your refrigerator. If noise is issuing from there, it is most likely a problem with the circulating fan in self-defrosting fridges. Replace the circulating fan according to your manual.