How did the Messenger of Allah (peace and blessings be upon him and his family) conclude the prescribed prayers? Did he make supplications afterward audibly or inaudibly?

A number of supplications and invocations have been reported from the Prophet (peace and blessings be upon him and his family) to be recited after closing the prayer with greetings (salam); it is recommended for the worshipper to recite them after the obligatory prayer. There is no objection to reciting them audibly, provided that this does not disturb or distract other worshippers. It has also been reported that the Prophet (peace and blessings be upon him and his family) used to recite the Muʿawidhat after every prayer—that is, Qul Huwa Allahu Ahad, Qul Aʿudhu bi Rabb al-Falaq, and Qul Aʿudhu bi Rabb al-Nas’ (recorded by Imam Ahmad in his Musnad and by Abu Dawud and an-Nasa’i in their respective Sunan).

ʿAli (may Allah be pleased with him) reported that the Prophet (peace and blessings be upon him and his family) said, “Whoever recites the verses of the Throne [Ayat al-Kursi] after each prescribed prayer will remain under the protection of Allah until the next prayer” (recorded by at-Tabarani in Al-Muʿjam al-Kabir with a good chain of transmission). In another hadith, Abu Huraira (may Allah be pleased with him) narrated that the Prophet (peace and blessings be upon him and his family) said, “Whoever glorifies Allah thirty-three times after every prayer, praises Allah thirty-three times, and declares Allah’s greatness thirty-three times, making ninety-nine in total, and completes one hundred by saying, ‘There is no deity except Allah alone; He has no partner. To Him belongs the dominion, and all praise, and He has power over all things,’ will be forgiven his sins, even if they are like the foam of the sea” (recorded by Bukhari and Muslim).

And Allah Almighty knows best.