How the pledge of allegiance is given in Islam

It is narrated from Sayyiduna Anas (may Allah be pleased with him) that he said: "I came to Madinah when Sayyiduna Abu Bakr (may Allah be pleased with him) had passed away and Sayyiduna Umar (may Allah be pleased with him) had been made caliph. So I said to Sayyiduna Umar (may Allah be pleased with him): Stretch out your hand so that I may pledge allegiance to you on the same terms on which I pledged allegiance to your companion before you, that is, on hearing and obeying, according to my ability."
Imam al-Tayalisi also narrated something similar through Hammad bin Salamah, at the end of which it says (explaining who is meant by "your companion"): "That is, the Prophet (peace and blessings be upon him) and Sayyiduna Abu Bakr al-Siddiq (may Allah be pleased with him)."

It is narrated from Sayyiduna Abu al-Afif (may Allah be pleased with him): I was present when, after the sorrowful passing of the Messenger of Allah (peace and blessings be upon him), Sayyiduna Abu Bakr al-Siddiq (may Allah be pleased with him) was taking the pledge of allegiance from the people. Groups of people would gather around him, and he would say to them: "Pledge allegiance to me on carrying out the commands of Allah Almighty and His Book, and then on hearing and obeying the commander." Abu al-Afif (may Allah be pleased with him) says: I was holding my whip, and in those days I was a youth who had reached puberty or was close to it. So when the people had left and he was alone, I came to him and said: "I pledge allegiance to you on obedience to Allah Almighty and His Book, and on hearing and obeying the commander." The narrator says: (On hearing this) he looked me up and down (carefully).
Imam al-Harith bin Muhammad bin Abi Usamah narrated it in his Musnad al-Harith.

It is narrated from Sayyidah Asma' bint Yazid (may Allah be pleased with her) that the Messenger of Allah (peace and blessings be upon him) called the believing women to bay'ah (the pledge of allegiance). Sayyidah Asma' (may Allah be pleased with her) said: "O Messenger of Allah! Will you not uncover your blessed hand to us (to take the pledge)?" He (peace and blessings be upon him) said: "Indeed, I do not shake hands with women."
Its chain is hasan (good).

Amr bin Atiyyah (may Allah have mercy on him) relates: "I came to Sayyiduna Umar (may Allah be pleased with him) and pledged allegiance at his hand while I was still a boy; this pledge was upon the Book of Allah and the Sunnah of His Prophet (peace and blessings be upon him), which is (entirely good) in our favour and (an obligation) binding upon us. He laughed (on hearing my firm words) and accepted my pledge."
Imam Musaddad bin Musarhad recorded this narration in his compilation.

It is narrated from Sayyidah Aishah (may Allah be pleased with her) that Hind bint Utbah bin Rabi'ah (may Allah be pleased with her) came to the Messenger of Allah (peace and blessings be upon him) to pledge allegiance, and he (peace and blessings be upon him) said: "Go and change the colour of your hands (with henna) and come back." She went and coloured her hands with henna, then she came again to the Messenger of Allah (peace and blessings be upon him), and he (peace and blessings be upon him) said: "I take your pledge on the conditions that you will not associate anything with Allah, you will not steal, and you will not commit fornication." She said (in astonishment): "Would a free, honourable woman commit fornication?" He (peace and blessings be upon him), mentioning a further condition, said: "And you will not kill your children for fear of poverty [Surah al-Mumtahinah: 12]." She said (alluding to the killing of her sons at Badr): "Have you left us any children that we might now kill them?" The female narrator says: Then she pledged allegiance to him (peace and blessings be upon him). At that time she was wearing two gold bracelets, and she asked: "What do you say about these two bracelets?" He (peace and blessings be upon him) said: "These are two live coals from the coals of Hell."
Imam Abu Ya'la recorded this narration in his Musnad. The imams have criticised the female narrator in its chain, Ghibtah Umm Amr; however, the other basic conditions of the pledge are established by explicit verses of the Noble Qur'an.