Rosh Chodesh Sivan: Beginning To Prepare
One should begin to prepare for Shavuot on Rosh Chodesh Sivan by intensifying his Torah study, and to draw on the holiness that was revealed on that day. (Avodat Yisrael – Inyanei Shavuot.)
One should review in the Torah what happened each day of Sivan on that particular day. (Ibid.)