The warhorn is found along with spear and arrow heads made of dragonglass, all wrapped in the black cloak of a brother of the Night's Watch. Sam and Grenn do not take notice of the warhorn, as they are more interested in the rare dragonglass weapons.
In the books
In the A Song of Ice and Fire novels, the warhorn and dragonglass cache is found by Jon Snow and Ghost. The warhorn is made from an auroch's horn and is banded with bronze. On closer examination the horn had proved cracked, and even after Jon cleaned all the dirt out, he was unable to get any sound from it. The rim is chipped as well, but Jon gives the horn to Sam anyway, since Sam likes to collect old things, even worthless ones. He tells Sam "Make a drinking horn out of it, and every time you take a drink you'll remember how you ranged beyond the Wall, all the way to the Fist of the First Men". Sam carries the warhorn all the way from the Fist to Castle Black, and from there to Oldtown; currently the horn is still in his possession.
So far in the novels, there is nothing to indicate that the broken warhorn has any special properties. However, there is a fan theory that the seemingly useless warhorn is in fact the legendary Horn of Winter, used many years ago by the King-Beyond-the-Wall Joramun to wake giants from the earth.