How did the Prophet (peace be upon him) perform Ruku` (bowing)? Did he do anything after Taslim (salutation of peace ending the Prayer)?
The Prophet (peace be upon him) used to straighten his back and place his hands firmly on his knees while performing Ruku`. He (peace be upon him) would make Istighfar (seeking forgiveness from Allah) three times after Salah was finished. He also used to say:
O Allah, You are the Grantor of security, and security comes from You. You are Blessing, O You Who have majesty and nobility)!''
Afterwards, he would rise up and say:
La ilaha illa Allah, wahdahu la shareeka lahu, lahul-mulku wa-lahul-hamdu, wa-huwa ‘ala kulli shai’in qadeer, la hawla wa-la quwwata illa billah, la ilaha illa Allah wa-la na‘budu illa iyyah, lahun-Ni‘matu wa-lahul-Fadl, wa-lahu ath-thanaa’u al-hasan, la ilaha illa Allah mukhliseena, lahud-Deena wa-law karihal-Kafiroon. Allahumma la mani‘a lima ‘atait wa-la mu‘ti lima mana‘t, wa-la yanfa‘u dhal-gaddu minkal-gadd. (None has the right to be worshipped except Allah, alone, without any partner. To Allah belong all sovereignty and praise and He is Omnipotent over all things. There is no might or power except with Allah. None has the right to be worshipped except Him and we worship none but Him. For Allah all favor, grace, and praise are due. None has the right to be worshipped but Allah and we are sincere in faith and devotion to Him although the disbelievers detest it. Oh Allah! None can grant what You have willed to prevent, and no wealth or majesty can benefit anyone, as from You is all wealth and majesty).
(Part No. 6; Page No. 429) The Prophet (peace be upon him) taught his Sahabah (Companions) to recite Tasbih (saying: "Subhan Allah [Glory be to Allah]"), Takbir (saying: "Allahu Akbar [Allah is the Greatest]") and Tahmid (saying: "Al-hamdu lillah [All praise is due to Allah]") after Salah. Each formula is recited thirty three times. They were taught to say : 'la ilah illa Allah wahdahu la sharika lahu lahu al-mulk wa lahu al-hamd wa huwa `ala kull shay'in qadir' (there is no deity worthy of worship except Allah Alone, He having no associate. His is the Dominion and due to Him is all praise and He has power over all things). They were also taught to recite Ayat-ul-Kursy (the Qur’anic Verse of the Throne, Surah Al-Baqarah, 2:255) and the last three chapters of the Qur'an (Surah Al-Ikhlas, Surah Al-Falaq and Surah Al-Nas). According to an authentic Hadith reported from the Prophet (peace be upon him), it is recommended that these last three Surahs be recited three times following the Fajr (Dawn) and Maghrib (Sunset) Prayers. It is also recommended to recite the following Dhikr (Remembrance of Allah) ten times after Fajr and Maghrib Prayers: 'la ilah illa Allah wahdahu la sharika lahu lahu al-mulk wa lahu al-hamd yuhyi wa yumit wa huwa `ala kull shay'in qadir' (there is no deity worthy of worship except Allah Alone, He has no associate. His is the Dominion and due to Him is all praise; He gives life and causes death and He has power over all things). This is also based on an authentic Hadith narrated from the Prophet (peace be upon him).May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.