Today - Tuesday - is the first day of the first month - Nissan!
The first day of Nissan was the last of the 8 inaugural days of the Mishkan (tabernacle) and the first day that Aaron served as Cohen Gadol (high priest) and his 4 sons as Cohanim.
That same day, two of them - Nadav and Avihu - brought an offering, not in accordance with Halacha, and were killed by a heavenly fire.
On that day, the heads of the 12 tribes started bringing their inaugural sacrifices, one prince each day. Some people have the custom of reading that days' sacrifices during the first 12 days of Nissan. This can be found in the Siddur as the Torah Reading for Chanuka.
One does not say Tachanun during the entire month of Nissan.
One may not fast during Nissan, with the following exceptions:
- Firstborns fast on Erev Pesach (tomorrow in 2 weeks).
- Fasting for distressingly bad dreams.
- Couples getting married during Nissan, even on Rosh Chodesh, even though on any other Rosh Chodesh the bride and groom do not fast.
Don't forget יַעֲלֶה וְיָבוֹא in Birkat Hamazon and the Amida.