Hajaar, the mother of Nabi Ismaa'eel a.s. and wife to Nabi Ibraaheem a.s. was the first to find the Zamzam Well at the heels of baby Ismaa'eel a.s. It is said that over time, the Zamzam Well was buried due to the wickedness of generations that came after its first discovery. That is, until the time of 'Abdul Muttalib, the grandfather of Prophet Muhammad, peace and blessings be upon him (s.a.w.).
One day while 'Abdul Muttalib was sleeping in Al-Hijr (a northern side of the Ka'bah), someone came to him and said,
"Dig Taibah."
"And what is Taibah?" 'Abdul Muttalib asked. But that someone left him without answering.
The next day, 'Abdul Muttalib returned to the same corner to sleep and the same thing happened again but this time he said,
"Dig Barrah."
"And what is Barrah?" 'Abdul Muttalib asked. But that someone left him without answering, again.
The day after next, 'Abdul Muttalib returned to the same corner to sleep again. The same someone came again and said,
"Dig Al-Madnoonah."
"And what is Al-Madnoonah?" 'Abdul Muttalib asked. But that someone left him again, without answering.
The following day, 'Abdul Muttalib returned again to the same corner to sleep. After he fell asleep, he came again and said,
"Dig Zamzam." "And what is Zamzam?" 'Abdul Muttalib asked.
"It (is a well) that never runs dry, and it is not dispraised (i.e. it is fresh and good). It is drink for the greater pilgrims (i.e. those who come for Umrah and Hajj). And it is situated between excrement and blood, at the eyehole of the Al-'Asim crow (i.e. the crow that has whiteness in its legs), at the village of the ants.
'Abdul Muttalib went in search of the Zamzam with an axe, accompanied by his only son at the time, Al-Haarith. Lo and behold, he saw the edge of the well and immediately magnified Allah SWT by exclaiming, "ALLAHU AKBAR!"
By the sound of his voice, the Quraish knew that he found what he had been looking for, and so they went to him. They said,
"Ya 'Abdul Muttalib, this indeed is the well of our father, Ismaa'eel, and we have a right over it." And they asked him to share the ownership of the Zamzam Well.
'Abdul Muttalib said, "I will not do so. This is a matter which I have been chosen and tasked to do."
Unsatisfied with his reply, they persisted, "Then do us justice, for we will not leave you alone but will argue with you over it."
'Abdul Muttalib said, "Then appoint anyone you wish and we will take the matter to him for judgment."
And they appointed the soothsayer of Banu Sa'd ibn Hudhaim, who lived in the border regions of Ash-Sham (around Syria and bordering lands).
They set out on their journey to Ash-Sham with a group of people from every subtribe of the Quraish. The journey was very far with a vast desert land ahead of them with no village or townships in between. A difficult journey, indeed!
At one point of the journey, 'Abdul Muttalib and his subtribe ran out of water. Their situation was so dire that they felt it would end in their deaths. Even though the other subtribes had water, they refused to share for fear of their own death.
'Abdul Muttalib said to his subtribe,
"I think that each man among you should now bury his own grave, using the strength he still has with him. Whenever a man among you dies, the others can push him into his hole and then bury him, until there remains one man, since it is better for one man to be lost (without a burial) than for the entire caravan to be lost."
Each man among his subtribe dug his grave and and then sat down, waiting for his death.
'Abdul Muttalib said to them,
"By Allah, for us to kill ourselves in this manner will not make us deserving of (praise) on earth, and we should not be weak like this. Perhaps Allah will provide us with water in some land (ahead of us), so prepare to move on."
So his subtribe prepared to continue their journey. Suddenly, when 'Abdul Muttalib made his camel stand up, a spring of fresh water gushed forth from underneath its hooves.
And all of them exclaimed, "ALLAHU AKBAR!"
They drank the water, filled their containers and invited the other Quraish subtribes to take some water.
The other subtribes drank, filled their containers and then said,
"By Allah, we will never again enter into a dispute with you regarding Zamzam, for the One Who has given you this water to drink in this barren land, is indeed the One Who gave you Zamzam to drink. So return to your water, rightly-guided."
They all returned to Makkah after that since there was no longer any need to go to the soothsayer. No one argued about 'Abdul Muttalib's right to have complete control over Zamzam Well after that incident.
Reference:
The Noble Life of The Prophet (peace be upon him), Volume I, Dr. 'Ali Muhammad As-Sallaabee