Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) said: When we sat with the Prophet (peace and blessings be upon him) for the tashahhud in prayer, we used to say: 'As-salamu 'alallahi qabla 'ibadihi' "Peace be upon Allah before His servants, peace be upon Jibra'il, peace be upon Mika'il, peace be upon so-and-so, peace be upon so-and-so." Then the Messenger of Allah (peace and blessings be upon him) said: "Indeed, Allah Himself is al-Salam (Peace). When one of you sits in prayer, let him say: 'At-tahiyyatu lillahi was-salawatu wat-tayyibatu, as-salamu 'alayka ayyuhan-nabiyyu wa rahmatullahi wa barakatuhu, as-salamu 'alayna wa 'ala 'ibadillahis-salihin' (All verbal, physical and financial acts of worship are for Allah. Peace be upon you, O Prophet, and the mercy of Allah and His blessings. Peace be upon us and upon all the righteous servants of Allah.) When a person says these words, the greeting reaches every righteous servant in the heavens and the earth. 'Ashhadu an la ilaha illallahu wa ashhadu anna Muhammadan 'abduhu wa rasuluhu' (I bear witness that there is no deity worthy of worship except Allah, and I bear witness that Muhammad (peace and blessings be upon him) is His servant and His Messenger.) Then, after that, let him ask whatever supplication he wishes."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2877
(a) Through another chain, a similar narration is also reported from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him); at its end it says: "Then let each of you make whatever supplication he wishes."
(b) Imam al-Bukhari (may Allah have mercy on him) recorded this narration in his Sahih through the chain of Musaddad from Yahya al-Qattan. Likewise, Mansur narrated it from Shaqiq, and at its end it says: "Then, after that, let him ask for whatever he wishes."
(c) The Messenger of Allah (peace and blessings be upon him) supplicated in his prayer in favour of certain peoples, and also supplicated against certain peoples, naming them; this subject will come in its proper place, if Allah wills.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2878
Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) said that in prayer a person should first recite the tashahhud, then send blessings upon the Prophet (peace and blessings be upon him), then supplicate for himself.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2879
It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) that the Prophet (peace and blessings be upon him), Abu Bakr and Umar (may Allah be pleased with them both), the three of them, went out. Abu Bakr (may Allah be pleased with him) had invited him (peace and blessings be upon him). They went out from his (Abu Bakr's) house towards the mosque of Madinah, the Prophet's Mosque. Abdullah (may Allah be pleased with him) was standing in prayer, reciting. Then he sat and recited the tashahhud, then he praised and glorified Allah abundantly, then he sent blessings upon the Prophet (peace and blessings be upon him), then he supplicated with great humility, while the Prophet (peace and blessings be upon him) stood listening attentively. He (peace and blessings be upon him) began to say: "Ask, and whatever you ask for will be given to you." Abu Bakr (may Allah be pleased with him) said: O Messenger of Allah, who is this? He (peace and blessings be upon him) said: "This is Abdullah, the son of Umm Abd (may Allah be pleased with him). Whoever would like to recite the Qur'an fresh, just as it was revealed, let him recite it the way Ibn Umm Abd (may Allah be pleased with him) was reciting."
Abu Bakr al-Siddiq and Umar (may Allah be pleased with them both) hurried to him, and Abu Bakr got ahead of Umar (may Allah be pleased with them both). Umar (may Allah be pleased with him) was certain that Abu Bakr (may Allah be pleased with him) had got ahead of him, so Umar (may Allah be pleased with him) said: He is always the first to every good deed.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2880