-During The days of Sefira, it is customary to exhibit some signs of mourning, as in this time period the 24,000 disciples of Rabbi Akiva perished. (See Talmud Yevamos 62b and Tur and Shulchan Aruch Siman 493)
It is customary not to get married during Sefira. Getting engaged is permissible.
It is customary not to take haircuts or shave facial hair during Sefira.It is customary not to listen to music or dance during Sefira (We will elaborate on this in more detail iy”H in the coming days)
-Though the time of Sefira is from Pesach until Shavuos, it is customary to only exhibit the signs of mourning for 33 of the 49 days.
Some people start from Pesach and cease the mourning on Lag B’Omer, while others only begin exhibiting the signs of mourning from the first day of Rosh Chodesh Iyar until three days before Shavuos (Sh’loshes Yemei HaGbalah)(See Shu”t Chasam Sofer Orach Chaim Siman 142 and Igros Moshe Orach Chaim Vol. 1 Siman 159 regarding if today’s days there exists any problems of “Lo TisGodedu” with people who observe different times of Sefira)
Some Poskim maintain that one may switch his/her “33 days” from year to year (Hataras Nedarim may be necessary in order to do this), while others are stringent and maintain that one must continually follow the same minhag each year (See Michtavim U’Ma’amarim from Rav Eliezer Menachem Mann Shach Zatzal Vol. 6 page 71 for the reasoning why changing would not be permitted.)