Hacham Ovadia Yosef, in his work Hazon Ovadia (Laws of Nissan, p. 3), records the widespread practice to conduct a special reading on each of the first thirteen days of the month of Nissan. Rosh Hodesh Nissan marks the date on which the Mishkan was erected and consecrated (in the year following the Exodus from Egypt), and on this day the twelve Nesi'im (tribal leaders) brought a special gift in honor of this occasion, as we read in the Book of Bamidbar (chapter 7). The Torah tells that on each of the first twelve days of Nissan a different tribal leader brought his offering. To commemorate this event, it is customary to read on each of the first twelve days of Nissan the verses in the Torah that describe the gift offered that day. On the thirteenth day of Nissan, the custom is to read the section immediately following the account of the Nesi'im's gifts, namely, the first four verses of Parashat Beha'alotecha (Bamidbar 8:1-4).
Some have the custom to read these verses from a Torah scroll, but our practice is to read them from a Humash. The reading should be done after the prayer service each morning, and Kaddish is recited upon the completion of the reading. It is proper to recite the "Yehi Rason" and "Ribono Shel Olam" prayers associated with this reading, which are printed in many Siddurim.