Fiqh-us-Sunnah Volume 5, Hajj and ‘Umrah, Fiqh 5.081.
A person drinking Zamzam water should intend and hope for healing, blessings and whatever is best for him in this life and in the hereafter. The Prophet (peace be upon him) said, “The water of Zamzam is (good) for whatever it is intended.”
Suwaid bin Saeed reported: “When the water of Zamzam was brought to Abdullah bin Al-Mobarak I saw that he drank a little, then turning his face towards the Ka’bah supplicated, ‘O Allah! Ibn Abi Al-Mawali told us on the authority of Mohammad bin Al-Monkader, who narrated from Jaber that the Messenger of Allah (peace be upon him) said, “The water of Zamzam is good for whatever one intends (while drinking it).” I intend to drink this water to spare myself from going thirsty on the Day of Judgment.’ Then he drank the rest of the water.” (Reported by Al-Baihaqi, and Ahmad with a sound chain of authorities)
Ibn ‘Abbas reported that the Prophet (peace be upon him) said, “The water of Zamzam is good for whatever one intends (while drinking it). If you drink it seeking healing, Allah will give you healing. If you drink it to satisfy your hunger, Allah will satisfy your hunger. If you drink it to quench your thirst, Allah will quench your thirst. Zamzam is a well dug by the angel Gabriel by which Allah quenched the thirst of Isma’il.” This was reported by AdDaraqutni and Al-Hakim who added, “And if you drink it seeking refuge with Allah, Allah will give you refuge.”
It is desirable that one should drink Zamzam water in three breaths, face the Qiblah, drink as much as possible, praise and thank and supplicate to Him as Ibn ‘Abbas did. Abu Molaikah reported: “A man came to Ibn ‘Abbas. He asked the man, ‘Where are you coming from?’ The man replied: ‘I am coming from the well of Zamzam.’ Ibn ‘Abbas asked him, ‘Did you drink of it as you are supposed to?’ “The man asked: ‘O Ibn ‘Abbas, how am I supposed to drink it?’ Ibn ‘Abbas replied: ‘When you drink its water you should face the direction of the Qiblah, remember Allah, drink it in three breaths, drink as much as you can, and praise and thank Allah when you finish drinking.’ The Prophet (peace be upon him) said, ‘A major difference between us and the hypocrites is that they do not drink their fill of the Zamzam water’.” (Reported by Ibn Majah, Ad-Daraqutni and Al-Hakim)
Ibn ‘Abbas used to supplicate Allah, whenever he drank Zamzam water: “Allahumma inni as’aluka ‘ilman nafi`an wa rizqan wasi’an wa shifa an min kuli da in (O Allah! Grant me beneficial knowledge, bountiful provision, and a healing from every disease).”