From Anas (may Allah be pleased with him): that the Messenger of Allah (peace and blessings be upon him) used to breathe three times while drinking. Agreed upon (al-Bukhārī and Muslim). That is: he would breathe outside the vessel.
١١١ - باب أدب الشرب واستحباب التنفس ثلاثا خارج الإناء وكراهة التنفس في الإناء واستحباب إدارة الإناء على الأيمن فالأيمن بعد المبتدئ
From Anas (may Allah be pleased with him): that the Messenger of Allah (peace and blessings be upon him) used to breathe three times while drinking. Agreed upon (al-Bukhārī and Muslim). That is: he would breathe outside the vessel.
And from Ibn ʿAbbās (may Allah be pleased with them both), who said: The Messenger of Allah (peace and blessings be upon him) said: "Do not drink in a single draught like the drinking of a camel; rather, drink in two or three (breaths). Mention the name of Allah when you drink, and praise Him when you finish." Narrated by al-Tirmidhī, who said: "A good (ḥasan) hadith."
And from Abū Qatādah (may Allah be pleased with him): that the Prophet (peace and blessings be upon him) forbade breathing into the vessel. Agreed upon (al-Bukhārī and Muslim). That is: breathing into the vessel itself.
And from Anas (may Allah be pleased with him): that the Messenger of Allah (peace and blessings be upon him) was brought milk that had been mixed with water, with a bedouin on his right and Abū Bakr (may Allah be pleased with him) on his left. He drank, then gave (it) to the bedouin, and said: "The one on the right, then the one on the right." Agreed upon (al-Bukhārī and Muslim). His words "shība" mean: it was mixed.
And from Sahl ibn Saʿd (may Allah be pleased with him): that the Messenger of Allah (peace and blessings be upon him) was brought a drink, and he drank from it. On his right was a boy, and on his left were elders. He said to the boy: "Will you permit me to give (it) to these (elders)?" The boy said: "No, by Allah, I will not give anyone precedence over myself for my share from you." So the Messenger of Allah (peace and blessings be upon him) placed it in his hand. Agreed upon (al-Bukhārī and Muslim). His words "tallahu" mean: he placed it. This boy was Ibn ʿAbbās (may Allah be pleased with them both).