This excerpt is taken from Sheikh Abu Hamza Abdul Khaliq Siddiqi's book Sahih Fazail-e-Amaal.
After turning the Salam for the praying person, one should loudly say الله أكبر, then say أستغفر الله three times. Then it is Sunnah to recite these supplications.
Reference: Sahih Bukhari, Book of Adhan, Chapter: Remembrance after Prayer, No: 841, 842. Sahih Muslim, Book of Mosques, Chapter: Remembrance after Supplication, No: 583.
➊ اللَّهُمَّ أَنْتَ السَّلَامُ، وَمِنْكَ السَّلَامُ، تَبَارَكْتَ ذَا الْجَلَالِ وَالإِكْرَامِ
"O Allah! You are Peace and from You comes peace, You are the Most Blessed, O Possessor of Glory and Honor."
Reference: Sahih Muslim, Book of Mosques, Chapter: Recommendation of Remembrance after Prayer, No: 1334.
➋ لَا إِلَهَ إِلَّا اللَّهُ، وَحْدَهُ لَا شَرِيكَ لَهُ، لَهُ الْمُلْكُ، وَلَهُ الْحَمْدُ، وَهُوَ عَلَى كُلِّ شَيْءٍ قَدِيرٌ، اللَّهُمَّ لَا مَانِعَ لِمَا أَعْطَيْتَ، وَلَا مُعْطِيَ لِمَا مَنَعْتَ، وَلَا يَنْفَعُ ذَا الْجَدِّ مِنْكَ الْجَدُّ
"There is no deity worthy of worship except Allah alone, He has no partner, His is the dominion and all praise is for Him, and He is over all things competent. O Allah! None can withhold what You give, and none can give what You withhold, and no wealth of the rich will benefit him against Your punishment."
Reference: Sahih Muslim, Book of Mosques, No: 13384.
➌ Sayyiduna Mu'adh bin Jabal (RA) narrates that the Messenger of Allah (SAW) took my hand and said: O Mu'adh! By Allah, I love you, then the Prophet (SAW) said: (Since you love me, I advise you) do not leave reciting this supplication after every obligatory prayer:
رَبِّ أَعِنِّي عَلَى ذِكْرِكَ وَشُكْرِكَ وَحُسْنِ عِبَادَتِكَ
"O my Lord! Help me to remember You, to be grateful to You, and to worship You in an excellent manner."
Reference: Sunan an-Nasa'i al-Kubra, Book of Prayer, No: 1226 - Mustadrak Hakim: 273/1 and 273/3, 274.
Hakim declared it authentic, and Dhahabi agreed with him.➍ Then say سبحان الله thirty-three (33) times, الحمد لله thirty-three (33) times, and الله أكبر thirty-three (33) times, completing the count of one hundred (100) with this supplication:
لَا إِلَهَ إِلَّا اللَّهُ وَحْدَهُ لَا شَرِيكَ لَهُ، لَهُ الْمُلْكُ وَلَهُ الْحَمْدُ وَهُوَ عَلَى كُلِّ شَيْءٍ قَدِيرٌ
"There is no deity worthy of worship except Allah alone, He has no partner, His is the dominion and all praise is for Him, and He is over all things competent."
Reference: Sahih Muslim, Book of Mosques, Chapter: Recommendation of Remembrance after Prayer, No: 597.
➎ After every prayer, recite Ayat al-Kursi قل هو الله أحد قل أعوذ برب الفلق and قل أعوذ برب الناس. It is recommended to recite these three Surahs three times each after Fajr and Maghrib prayers.
Reference: Sunan Abu Dawood, Chapters of Witr, Chapter on Seeking Forgiveness, No: 1523 - Mustadrak Hakim: 1/253 - Sahih Ibn Hibban, No: 2347,
Hakim and Ibn Hibban declared it authentic.➏ After Maghrib and Fajr prayers, it is recommended to recite the following Tasbih (glorifications) ten times after the aforementioned remembrances:
لَا إِلَهَ إِلَّا اللَّهُ وَحْدَهُ لَا شَرِيكَ لَهُ، لَهُ الْمُلْكُ وَلَهُ الْحَمْدُ یحی ویمیت وَهُوَ عَلَى كُلِّ شَيْءٍ قَدِيرٌ
"There is no deity worthy of worship except Allah, He is Alone, He has no partner, His is the dominion and to Him belongs all praise, He gives life and causes death, and He is over all things competent."
➐ It is narrated from Umm Salamah (may Allah be pleased with her) that when the Prophet of Mercy (peace be upon him) finished the Fajr prayer, he would say:
اللَّهُمَّ إِنِّي أَسْأَلُكَ عِلْمًا نَافِعًا، وَرِزْقًا طَيِّبًا، وَعَمَلًا مُتَقَبَّلًا
"O Allah! I ask You for beneficial knowledge, pure provision, and deeds accepted by You."
Reference: Sunan Ibn Majah, Book of Establishing the Prayers and the Sunnah in them, Hadith No: 925 -
Al-Albani (may Allah have mercy on him) authenticated it.It should be noted that reciting these remembrances and glorifications is recommended, and there are other Sunnah remembrances as well.