The Omer count begins on the night of the sixteenth of Nissan, as it says, You shall count for yourself seven weeks; from when the sickle begins [to cut] the standing crop shall you begin to count seven weeks (Devarim 16:9-10). “From when the sickle begins [to cut] the standing crop” refers to the cutting of the Omer, for the first harvest of the yearly produce is designated for the Omer offering. And the Omer is harvested on the night after the first day of Pesach, which is the sixteenth of Nissan. That is when the count begins.
One must count at night, because the Torah says about the Omer count, Seven weeks; they shall be complete (VaYikra 23:15), meaning whole. As is well known, a calendar day consists of night and day, and if we want to include all the nights and days of the seven weeks, we must start counting on the night of the sixteenth of Nissan (Menachot 66a). And in order to include all [twenty-four] hours of the day, it is worthy to count at the beginning of the night. People are careful about this especially at the beginning of the count, on the first night, so that the count will include every hour of the seven weeks. Nonetheless, it is meritorious to count at the beginning of the night every night, so that each day’s count will be whole and will include the entire 24-hour period.
Even though it is best to count at the beginning of the night, one is not obligated to do so. Therefore, one who needs to pray Ma’ariv must do so before counting the Omer. After all, the rule is that more frequent mitzvot take precedence over less frequent ones, and the mitzvot of reading the Shema and praying Ma’ariv are in practice all year round, making them more frequent than the Omer count (Chok Natan; see B.H. 489:1, s.v. achar).
In order to avoid delaying the count, many [poskim] suggest that we count immediately after the “Titkabel” Kaddish, with which we end the Amidah (standing prayer), before Aleinu, which is an additional prayer. This is found in the Mishnah Berurah (489:2) and Nahar Mitzrayim, and most Jews follow this custom, including all Ashkenazim and most Jews who come from North Africa. Nonetheless, many Jews who pray according to the Sefardic version of prayer count after Aleinu, in order to first finish everything that is usually said in the Ma’ariv service.