Easiest way to tell is to listen closely and see if you can identify what part of the case it is. It could be one of the computers fans, it could be a hard drive, it could be the fan inside the power supply or attached to the video card. It is most likely one of these moving components however.
Only other way to determine the source is to swap out components that you suspect might be responsible and then see if the noise persists.
Keep in mind that the squeaking might not indicate an imminent system failure. It could be a case fan or something else that is relatively minor.