As this picture of a Rabbi teaching in a Yeshiva in Bnei Brak illustrates, today's lessons are taught by means of notes and books. However, the question of the emergence and transmission of traditions in rabbinic times remains unsettled. While Catherine Hezser assumes them to have originated in discussions between Rabbis and their collegues, students and community members who approached them for legal advice (pp. 38, 39), Martin S. Jaffee argues for the pre-existence of “written texts which served either as sources for learned exposition or as scripts for public declamation.” (p. 56).
Probably the most prominent example thereof is the tractate Pirkei Avot, which appears in the Mishnah and begins with a description of how the Torah was transmitted by Moses, who received it from God at Mount Sinai, to Yehoshua, who passed it on until the chain of transmission reaches Hillel and Shammai, thereby claiming the Oral Torah of the Rabbis to be revealed alongside the written one at Mount Sinai.
The internet appearance “Kikar Ha-Shabbat”, intended to replace the crossing Kikar Ha-Shabbat in Jerusalem as the place, where Charedim (Ultraorthodox Jews) meet in order to exchange relevant information and demonstrate for their concerns, exemplifies how rabbinic teachings nowadays still are sometimes presented in the oral form. There you can find videos and audio files dealing with halakhic and aggadic topics, taught by contemporary Rabbis.