Everything said in the prayer, in order, from the takbir to the salam. Wordings differ slightly between schools; these are widely used forms. For the rules of prayer, ask a scholar you trust.
To start the prayer, and at each change of positionاللَّهُ أَكْبَرُallaahu akbarAllah is the Greatest.
2. Opening praise (thanaa’)
After the first takbirسُبْحَانَكَ اللَّهُمَّ وَبِحَمْدِكَ، وَتَبَارَكَ اسْمُكَ، وَتَعَالَى جَدُّكَ، وَلَا إِلَٰهَ غَيْرُكَsubḥaanaka llaahumma wa-biḥamdika, wa-tabaaraka smuka, wa-taʿaalaa jadduka, wa-laa ilaaha ghayrukGlory be to You, O Allah, and praise. Blessed is Your name, high is Your majesty, and there is no god but You.
3. Seeking refuge (taʿawwudh)
Before reciting the Quranأَعُوذُ بِاللَّهِ مِنَ الشَّيْطَانِ الرَّجِيمِaʿuudhu billaahi mina sh-shayṭaani r-rajiimI seek refuge in Allah from Satan, the rejected.
4. Basmala
Before Al-Fatihaبِسْمِ اللَّهِ الرَّحْمَٰنِ الرَّحِيمِbismi llaahi r-raḥmaani r-raḥiimIn the name of Allah, the Most Gracious, the Most Merciful.
5. In rukuʿ (bowing)
While bowing, usually three timesسُبْحَانَ رَبِّيَ الْعَظِيمِsubḥaana rabbiya l-ʿaẓiimGlory be to my Lord, the Most Great.
6. Rising from rukuʿ
While standing up from bowingسَمِعَ اللَّهُ لِمَنْ حَمِدَهُsamiʿa llaahu liman ḥamidahAllah hears the one who praises Him.
7. Standing after rukuʿ
Once standing straight (also said without وَ)رَبَّنَا وَلَكَ الْحَمْدُrabbanaa wa-laka l-ḥamdOur Lord, and to You belongs all praise.
8. In sujud (prostration)
In each prostration, usually three timesسُبْحَانَ رَبِّيَ الْأَعْلَىsubḥaana rabbiya l-aʿlaaGlory be to my Lord, the Most High.
9. Between the two prostrations
Sitting between the two prostrationsرَبِّ اغْفِرْ لِيrabbi ghfir liiMy Lord, forgive me.
10. Tashahhud
Sitting after the second rakʿah and at the end of the prayerالتَّحِيَّاتُ لِلَّهِ وَالصَّلَوَاتُ وَالطَّيِّبَاتُ، السَّلَامُ عَلَيْكَ أَيُّهَا النَّبِيُّ وَرَحْمَةُ اللَّهِ وَبَرَكَاتُهُ، السَّلَامُ عَلَيْنَا وَعَلَى عِبَادِ اللَّهِ الصَّالِحِينَ، أَشْهَدُ أَنْ لَا إِلَٰهَ إِلَّا اللَّهُ، وَأَشْهَدُ أَنَّ مُحَمَّدًا عَبْدُهُ وَرَسُولُهُat-taḥiyyaatu lillaahi waṣ-ṣalawaatu waṭ-ṭayyibaat, as-salaamu ʿalayka ayyuha n-nabiyyu wa-raḥmatu llaahi wa-barakaatuh, as-salaamu ʿalaynaa wa-ʿalaa ʿibaadi llaahi ṣ-ṣaaliḥiin, ashhadu an laa ilaaha illa llaah, wa-ashhadu anna muḥammadan ʿabduhuu wa-rasuuluhAll greetings, prayers and good things are for Allah. Peace be upon you, O Prophet, and the mercy of Allah and His blessings. Peace be upon us and upon the righteous servants of Allah. I bear witness that there is no god but Allah, and I bear witness that Muhammad is His servant and messenger.
11. Durood (prayer for the Prophet ﷺ)
In the last sitting, after the tashahhudاللَّهُمَّ صَلِّ عَلَى مُحَمَّدٍ وَعَلَى آلِ مُحَمَّدٍ، كَمَا صَلَّيْتَ عَلَى إِبْرَاهِيمَ وَعَلَى آلِ إِبْرَاهِيمَ، إِنَّكَ حَمِيدٌ مَجِيدٌ. اللَّهُمَّ بَارِكْ عَلَى مُحَمَّدٍ وَعَلَى آلِ مُحَمَّدٍ، كَمَا بَارَكْتَ عَلَى إِبْرَاهِيمَ وَعَلَى آلِ إِبْرَاهِيمَ، إِنَّكَ حَمِيدٌ مَجِيدٌallaahumma ṣalli ʿalaa muḥammadin wa-ʿalaa aali muḥammad, kamaa ṣallayta ʿalaa ibraahiima wa-ʿalaa aali ibraahiim, innaka ḥamiidun majiid. allaahumma baarik ʿalaa muḥammadin wa-ʿalaa aali muḥammad, kamaa baarakta ʿalaa ibraahiima wa-ʿalaa aali ibraahiim, innaka ḥamiidun majiidO Allah, send Your grace on Muhammad and on the family of Muhammad, as You sent Your grace on Ibrahim and on the family of Ibrahim; You are Praiseworthy, Glorious. O Allah, bless Muhammad and the family of Muhammad, as You blessed Ibrahim and the family of Ibrahim; You are Praiseworthy, Glorious.
12. Ending the prayer (taslim)
Turning the head to the right, then to the leftالسَّلَامُ عَلَيْكُمْ وَرَحْمَةُ اللَّهِas-salaamu ʿalaykum wa-raḥmatu llaahPeace and the mercy of Allah be upon you.