Ibn 'Abbas (May Allah be pleased with them) reported

Ibrahim (ﷺ) brought his wife and her son Isma'il (ﷺ), while she was suckling him, to a place near the Ka'bah under a tree on the spot of Zamzam, at the highest place in the mosque. In those days, there was no human being in Makkah, nor was there any water. So he made them sit over there and placed near them a leather bag containing some dates, and a small water-skin containing some water, and set out homeward. Isma'il's mother followed him saying: "O Ibrahim! Where are you going, leaving us in this valley where there is no person whose company we may enjoy, nor is there anything (to enjoy)?" She repeated that to him many times, but he did not look back at her. Then she asked him: "Has Allah commanded you to do so?" He said: "Yes." She said: "Then He will not neglect us." She returned while Ibrahim proceeded onwards. Having reached the Thaniya, where they could not see him, he faced Ka'bah, raised his both hands and supplicated: "O our Rubb! I have made some of my offspring to dwell in an uncultivable valley by Your Sacred House (the Ka'bah at Makkah) in order, O our Rubb, that they may perform As-Salat (Iqamat-as-Salat). So fill some hearts among men with love towards them, and (O Allah) provide them with fruits so that they may give thanks." (14:37).

Isma'il's mother went on suckling Isma'il and drinking from the water which she had. When the water in the water-skin had all been used up, she became thirsty and her child also became thirsty. She started looking at Isma'il, tossing in agony. She left him, for she could not endure looking at him, and found that the mountain of As-Safa was the nearest mountain to her on that land. She stood on it and started looking at the valley keenly so that she might see somebody, but she could not see anybody. Then she descended from As-Safa, and when she reached the valley, she tucked up her robe and ran in the valley like a person in distress and trouble till she crossed the valley and reached Al-Marwah mountain where she stood and started looking, expecting to see somebody, but she could not see anybody. She repeated that (running between As-Safa and Al-Marwah) seven times." Ibn 'Abbas further related: The Prophet (ﷺ) said, "This is the source of the tradition of the Sa'y - i.e., the going of people between the two mountains. When she reached Al-Marwah (for the last time), she heard a voice and she exclaimed: 'Shshs!' (Silencing herself) and listened attentively. She heard the voice again and said: 'O (whoever you may be) You have made me hear your voice; have you any succour for me?' And behold! She saw an angel at the place of Zamzam, digging the earth with his heel (or with his wing), till water flowed out from that place. She started to make something like of a basin around it, using her hands in this way and began to fill her water- skin with water with her hands, and the water was flowing out until she had scooped some of it." The Prophet (ﷺ) further said, "May Allah bestow mercy on Isma'il's mother! Had she let the Zamzam flow without trying to control it (or had she not scooped in that water) while filling her water-skin, Zamzam would have been a stream flowing on the surface of the earth." The Prophet (ﷺ) further added, "Then she drank (water) and suckled her child. The angel said to her: 'Do not be afraid of being neglected, for this is the site on which the House of Allah will be built by this boy and his father, and Allah will never let neglected His people.' The House of Allah (the Ka'bah) at that time was on a high place resembling a hillock, and when torrents came, they flowed to its right and left. She continued living in that way till some people from the tribe of Jurhum passed by her and her child. As they were coming from through the way of Kada', in the lower part of Makkah where they saw a bird that had a habit of flying around water and not leaving it. They said: 'This bird must be flying over water, though we know that there is no water in this valley.' They sent one or two messengers who discovered the source of water, and returned to inform them of the water. So, they all came towards the water." The Prophet (ﷺ) added, "Isma'il's mother was sitting near the water. They asked her: 'Do you allow us to stay with you?' She replied: 'Yes, but you will have no right to possess the water.' They agreed to that." The Prophet (ﷺ) further said, "Isma'il's mother was pleased with the whole situation as she used to love the company of the people. So, they settled there, and later on they sent for their families who came and settled with them. The child (i.e., Isma'il) grew up and learnt Arabic from them (his virtues) caused them to love and admire him as he grew up, and when he reached the age of puberty, they gave him one of their daughters in marriage. After Isma'il's mother had died, Ibrahim came after Isma'il's marriage in order to see his family that he had left before, but he did not find Isma'il there. When he asked Isma'il's wife about him, she replied: 'He has gone in search of our livelihood.' Then he asked her about their way of living and their condition, and she replied complaining to him: 'We are living in hardship, misery and destitution.' He said: 'When your husband returns, convey my salutations to him and tell him to change the threshold of the door of his house.' When Isma'il came, he seemed to have perceived something unusual. He asked his wife: 'Did anyone visit you?' She replied: 'Yes, an old man of such and such description came and asked me about you and I informed him, and he asked about our state of living, and, I told him that we were living in hardship and poverty.' Thereupon Isma'il said: 'Did he advise you anything?' She replied: 'Yes, he told me to convey his salutations to you and to change the threshold of your door.' Isma'il said: 'That was my father, and he has ordered me to divorce you. Go back to your family.' So Isma'il divorced her and married another woman from amongst them (Jurhum). Then Ibrahim stayed away from them for a period as long as Allah wished, and called on them again but did not find Isma'il. So he came to Isma'il's wife and asked her about him. She said: 'He has gone in search of our livelihood.' Ibrahim asked her about their sustenance and living: 'How are you getting on?' She replied: 'We are prosperous and well off.' Then she praised Allah, the Exalted. Ibrahim asked: 'What kind of food do you eat?' She said: 'Meat.' He said: 'What do you drink?' She said: 'Water.' He said, 'O Allah! Bless their meat and water!"' The Prophet (ﷺ) added, "At that time they did not have grain, and if they had grain, he would have also invoked Allah to bless it." The Prophet (ﷺ) further said, "If somebody has only these two things as his sustenance, his health and disposition will be badly affected because these things do not suit him unless he lives in Makkah." The Prophet (ﷺ) added, "Then Ibrahim said to Isma'il's wife, 'When your husband comes, give my regards to him and tell him that he should keep firm the threshold of his door.' When Isma'il came back, he asked his wife: 'Did anyone call on you?' She replied: 'Yes, a good looking old man came to me.' She praised him and added: 'He asked about you, and I informed him, and he asked about our livelihood and I told him that we were in good condition.' Isma'il asked her: 'Did he give you a piece of advice?' She said: 'Yes, he told me to convey his regards to you and ordered that you should keep firm the threshold of your door.' On that Isma'il said: 'He was my father and you are the threshold of the door. He has ordered me to keep you with me.' Then Ibrahim stayed away from them for a period as long as Allah wished and called on them afterwards. He saw Isma'il under a tree near Zamzam, sharpening his arrows. When he saw Ibrahim, he rose up to welcome him, and they greeted each other as a father does with his son or a son does with his father. Ibrahim said: 'O Isma'il! Allah has given me an order.' Isma'il said: 'Do what your Rubb has commanded you to do.' Ibrahim asked: 'Will you help me?' Isma'il said: 'I will help you.' Ibrahim said: 'Allah has ordered me to build a house here, pointing to a hillock higher than the land surrounding it."' The Messenger of Allah (ﷺ) added, "Then they raised the foundations of the House (i.e., Ka'bah). Isma'il brought the stones and Ibrahim was building (the house). When the walls became high, Isma'il brought stone and placed it for Ibrahim who stood over it and carried on building the House, while Isma'il was handing over the stones to him, both of them prayed: 'O our Rubb! Accept this service from us! Verily, You are the All- Hearer and the All-Knower."'

[Al-Bukhari].

There are some more narrations about this incident, some adding details and some with minor variations in the wordings.