Standing, after the takbir, you recite Al-Fatiha, then a surah in the first two units (for the later ones, see “Unit by unit”).
You can learn Al-Fatiha word by word, with its transliteration, in the Namilo app.
The schools differ on the Fatiha in units 3 and 4, on the Fatiha behind an imam, and on the surah that follows it: their views and the hadiths are in the step. Awaiting review.
Standing in prayer: where the schools differ
In the third and fourth units of the obligatory prayers: from Abu Qatada, the Prophet ﷺ recited at Dhuhr the Fatiha and two surahs in the first two units, and the Fatiha in the last two, and likewise at Asr (al-Bukhari 776 (authentic: reported in the Sahih of al-Bukhari)); and “no prayer for whoever does not recite the Fatiha” (al-Bukhari 756 (authentic: reported in the Sahih of al-Bukhari)). According to az-Zuhayli (al-Fiqh al-Islami wa Adillatuh, vol. 2, pp. 881 and 905), the Fatiha is obligatory there in the Shafi'i school, and in the Maliki and Hanbali schools for the imam and for one praying alone; in the Hanafi school, it is recommended there, and one may also glorify Allah three times (tasbih) or remain silent for the time it takes to recite it.
The surah after the Fatiha: the same hadith of Abu Qatada (al-Bukhari 776 (authentic: reported in the Sahih of al-Bukhari)) places it in the first two units; from Abu Sa'id, “we were commanded to recite the Fatiha and whatever is easy” (Abu Dawud 818 (authentic according to al-Albani and Muhyi ad-Din ‘Abd al-Hamid; weak chain according to Shu‘ayb al-Arna’ut; weak according to Zubair Ali Zai)); and Abu Hurayra said: “If you add nothing to the Fatiha, it suffices; if you add, it is better” (al-Bukhari 772 (authentic: reported in the Sahih of al-Bukhari)). According to az-Zuhayli (same work, vol. 2, p. 882), this surah is obligatory (wajib) in the Hanafi school, and sunnah for the majority of scholars.
Behind an imam: in one transmission of the hadith of Abu Musa (Muslim 404 (no. 905 in the fawazahmed0 edition) (authentic: reported in the Sahih of Muslim)), the Prophet ﷺ says “when he recites, be silent”; Muslim says he holds authentic the hadith of Abu Hurayra that also reports it, without having placed it there. In at-Tirmidhi 312 (authentic according to Ahmad Muhammad Shakir, al-Albani and Zubair Ali Zai), from Abu Hurayra, the Prophet ﷺ asked after a prayer recited aloud whether anyone had recited with him; a man said yes, and he said: “I was saying to myself: why am I being contended with over the Quran?”; and the people stopped reciting with him in those prayers (some narrators attribute this last sentence to az-Zuhri). At-Tirmidhi adds there that this hadith does not contradict those who recite behind the imam. From Jabir, the Prophet ﷺ said: “Whoever has an imam, the imam’s recitation is his recitation” (Ibn Majah 850 (good according to al-Albani and Muhammad Fu’ad ‘Abd al-Baqi; weak according to Zubair Ali Zai)). And according to Muslim 395 (no. 878 in the fawazahmed0 edition) (authentic: reported in the Sahih of Muslim), Abu Hurayra told whoever prayed behind the imam: “Recite it to yourself.”
The schools, according to al-Mawsu'a al-Fiqhiyya (cited by islamweb.net, fatwa 277168): behind an imam, the Fatiha is obligatory in the Shafi'i school, in prayers recited aloud as in those recited silently; one does not recite behind the imam in the Hanafi school, even in silent prayers; in the Maliki and Hanbali schools, it is not obligatory. Malik says that the practice among them is to recite behind the imam when he recites silently, and not to recite when he recites aloud (the Muwatta of Malik 191 (numbering of the fawazahmed0 edition) (authentic as the saying of a Companion (mawquf), according to Salim al-Hilali)). At-Tirmidhi reports that Ahmad held that “no prayer for whoever does not recite the Fatiha” refers to one praying alone, and nevertheless chose to recite behind the imam, without leaving out the Fatiha (at-Tirmidhi 312 (authentic according to Ahmad Muhammad Shakir, al-Albani and Zubair Ali Zai)).
The basmala is numbered 1 here, as in the Hafs reading. In prayer, the schools do not all say it the same way: aloud, silently, or not at all in the obligatory prayer. Follow what you were taught.
Awaiting review by a scholar: the views of the schools are reported from the works cited, without choosing any of them. For your own practice, follow what you were taught or ask a person of knowledge.