The story has been told many times. The detector had an annoying and remarkably intransigent "hiss" and Penzias and Wilson knew it was the detector, since the hiss didn't change as they pointed their antenna at different places in the sky.  A radio hiss can be converted into a temperature: a red-hot coal has a temperature of a few thousand degrees Celsius but this hiss was microwave-hot, putting it just a few degrees above absolute zero.