If you can visualize the site of the bleed, you can cauterize the vessel.  This can be done with silver nitrate or electrocautery.  If you cannot visualize the specific site or vessel to be cauterized, you can place an anterior nasal pack:

Fig 5. (Images obtained from Kucik, C.J. & Clenney, T. Management of Epistaxis. American Family Physician. 71(2). Jan 2005)

In your patient, cautery successfully stops the bleeding.  He may safely go home, but should be seen again in two to three days to assess for recurrence and the health of the cautery site. 

What should the astute physician also do to prevent further epistaxis?