The First Day of Rosh Hashanah
Shabbat, September 16/ 1 Tishrei
It is best to rise before dawn on Rosh Hashanah (5:54 a.m.) or at least before sunrise (7:07 a.m.).
Some men customarily immerse in the mikvah again before the morning prayers. Especially the Chazanim, Kohanim, and those who will blow the shofar.
Melodies in the Prayers
The chazzan should not deviate from the nigunim (songs) that are customary in the community by singing melodies that he believes are nicer. This can disturb the concentration of the congregants and cause them to not pray properly. Neither should one try to show off his chazzanut on this awesome day. The main thing is for the chazzan to have kavana (concentration) in his heart.
Praying Alone
One who is praying alone is not obligated to recite the piyutim (poems) that are normally recited during the repetition of the Amidah but may do so if he wishes.
Psalm 130
When reciting Psalm 130 after Yishtabach during the Ten Days of Repentance, it is customary in some communities to open the ark and recite the verses responsively after the Chazzan. The Chabad custom, however, is to recite it but not responsively, and the ark is not opened.
No Hallel
Hallel is not recited on Rosh Hashanah and Yom Kippur because these are days of judgment.
