How would one know if ones jaw is broken?

Confirm Jaw Broken. An x-ray, such as a panograpnic view showing both condyles of each temporo-mandibular joint, "tmj".
Radiographs. X-rays will show whether or not the jaw is broken. Other symptoms, while not conclusive on their own would suggest a strong possibility of a broken jaw: severe pain, swelling, numbness, and the sudden inability to close your teeth together normally after a blow to the jaw or face.
Sudden bite shift. The most obvious clinical sign is a sudden shift in your bite, often accompanied by mouth bleeding. An x-ray would confirm or refute the diagnosis. See an oral surgeon to help evaluate.