In principle a nosebleed is treated in the same manner. Almost all nosebleeds occur from the septum, the central partition that separates the nostrils.
This is made of cartilage (gristle). It has a rich blood supply, chiefly of smaller blood vessels. To control bleeding from this, grasp the fleshy portion of the nose firmly between the thumb and forefinger. and keep it compressed for five to ten minutes.