To quickly flesh out what rosends said in their comment, the Oral Torah was transmitted from court to court. The full list is recorded here. There were study halls and the men would be there often, learning what we are learning now, but in oral form, directly from the mouths of the teachers (the teachers would keep written notes, and students would make their own personal notes). Rambam writes:
רבינו הקדוש חיבר המשנה. ומימות משה רבינו ועד רבינו הקדוש לא חיברו חבור
שמלמדין אותו ברבים בתורה שבעל פה. אלא בכל דור ודור ראש בית דין או נביא
שהיה באותו הדור כותב לעצמו זכרון השמועות ששמע מרבותיו והוא מלמד על פה
ברבים. וכן כל אחד ואחד כותב לעצמו כפי כחו מביאור התורה ומהלכותיה כמו
ששמע. ומדברים שנתחדשו בכל דור ודור בדינים שלא למדום מפי השמועה אלא
במדה משלש עשרה מדות והסכימו עליהם בית דין הגדול.
Rabbenu Hakadosh composed the Mishnah. From the days of Moses, our
teacher, until Rabbenu Hakadosh, no one had composed a text for the
purpose of teaching the Oral Law in public. Instead, in each
generation, the head of the court or the prophet of that generation
would take notes of the teachings which he received from his masters
for himself, and teach them verbally in public. Similarly, according
to his own potential, each individual would write notes for himself of
what he heard regarding the explanation of the Torah, its laws, and
the new concepts that were deduced in each generation concerning laws
that were not communicated by the oral tradition, but rather deduced
using one of the thirteen principles of Biblical exegesis and accepted
by the high court.
Our tradition is replete with references to Torah study halls all the way back in time. An example would be the story of Hillel in Yoma 35b, who would attend the study hall of Shamaya and Avtalyon (and the famous story of how he could not afford entry one day and almost died in the snow on the roof, because he climbed up there to look through the skylight).
Another example is from the days of King Chizkiyahu, who issued a strong decree for people to remain in the study hall (Sanhedrin 94b)
Note, we have a principle of "yeridat hadorot". The rest of the world scoffs at this idea "people have been saying the youth are degenerate for all time, ignore it..." is the cynical take of this fact. We take this fact literally - every generation has become more debased, the holiness and strength of the human being in general has declined over time. The reason I mention this is to explain that the study of Torah was on a much higher level back then, even among the simple folk, not on a lower level as the question seems to think is more reasonable.
E.g. In the days of King Chizkiyahu:
מגבת ועד אנטיפרס ולא מצאו תינוק ותינוקת איש ואשה שלא היו בקיאין בהלכות
[They searched] from Gevat to Antipatris and did not find a male child, or a female
child, a man, or a woman who was not expert in the laws of ritual
purity and impurity. (Sanhedrin 94b)