How did R. Ya'akov Kamenetzky acquire his proficiency in Hebrew language, grammar and trope?

From books, of course, at least initially.

Here is an interesting excerpt from his son's Making of a Godol:


Chaim Zvi Lerner (1815-1889)

By : Herman Rosenthal Max Rosenthal

Russian grammarian and teacher of Hebrew; born at Dubno 1815; died at Jitomir 1889. His early education in Bible and Talmud he received from his father. At the age of thirteen he was married. In 1833, when Wolf Adelsohn went to Dubno and gathered around him a circle of Maskilim, to whom he taught Hebrew grammar and philosophy, Lerner became one of his disciples. He went to Odessa in 1835 and entered the model school of Bezaleel Stern, where Simḥah Pinsker was his teacher in Hebrew grammar. In the same school he also acquired a thorough knowledge of the Russian, German, French, and Italian languages. In 1838 Lerner returned to Dubno and became a teacher of Hebrew; from 1841 to 1849 he taught in Radzivilov; on Nov. 16 of the latter year he was appointed government teacher of the Jewish public school of Berdychev; and in 1851 he was appointed teacher of Hebrew at the rabbinical school of Jitomir, in which position he remained until the school was closed by the government (July 1, 1873).

Lerner's reputation among Hebrew grammarians was founded on his "Moreh ha-Lashon." It is written in a pure, popular Hebrew, and follows the system of grammar of European tongues, enabling the student to acquire the language more easily than did the works of his predecessors. The first edition appeared in 1859; six editions were issued during Lerner's lifetime; and many more have appeared since his death. Lerner was criticized for having adopted his methods from his teacher Pinsker; he himself acknowledged his indebtedness in the second edition of his work (p. 136, note).

Besides this grammar, Lerner wrote "Diḳduḳ Lashon Aramit" (Warsaw, 1875), an Aramaic grammar; "Ma'amar Toledot ha-Diḳduḳ" (Vienna, 1876); and a translation of S. D. Luzzatto's "Diḳduḳ Leshon Talmud Babli" (St. Petersburg, 1880). He left in manuscript: "Yalḳut," a collection of commentaries on the Bible and Rashi, together with critical and literary articles; "Arba' Middot," on the Baraita of the thirty-two Middot; and a Hebrew translation of Young's "Night Thoughts" and other poems.

Bibliography: Ha-Meliẓ, 1889, Nos. 76-79;
Sokolov, Sefer ha-Shanah, i. 62;
idem, Sefer Zikkaron, p. 66.H. R. M.

At least one of the books he read, presumably the "extremely intricate Hebrew grammar book" can be download or read here. Not bad for a 13 year old, huh?