Roman children learned Latin as their native language; school texts which survive are therefore from situations where speakers of other languages (usually Greek) needed to learn Latin as older students – generally for use in business, the law, or travel.
Eleanor Dickey’s book Learning Latin the Ancient Way: Latin Textbooks from the Ancient World (Cambridge University Press 2016) is a great source of texts in the original and translation, plus short and valuable discussion of how the texts were used and what they reveal about education in the ancient Roman world. (I’m really grateful to Katherine McDonald at the University of Exeter for pointing me to it.)
Greek speakers, of course, had to learn the Latin alphabet before they could begin to read the language (although some students seem to have learned Latin purely orally, presumably for contexts where reading it would be unnecessary). Dickey says (p. 119) that students learned by repeatedly copying the letter forms and saying them aloud. The letters usually had the following names (Dickey p. 120):
a, be, ce, de, e, ef, ge, ha, i, ka, el, em, en, o, pe, qu, er, es, te, u, ex
(y & z often had no name, but were sometimes referred to as y graeca and zeta).
French speakers will note similarities with the modern French letter names.
For more on the pronunciation of Latin as a native language, see W. Sidney Allen, Vox Latina: The Pronunciation of Classical Latin (ed. 2, Cambridge University Press, 1978).