According to minhag Ashkenaz we read 3 aliyos every day from the korbanos of the Nsi’im. On the first day, call up a cohen and read from Vayhi b’vom klos Moshe…until …lachanukas hamizbayach. Then, the levi and yisroel split the korban of the first day. (Rama 1 – MB 3)
On the second day, the cohen and levi split the korban of the second nossi. The yisroel reads the entire korban of the third nossi. On the third day, the cohen and levi split the korban of the third nossi and the yisroel reads the entire korban of the fourth nossi. This pattern continues each day. (ShA 1 – Rama 1)
On the eighth day, the cohen and levi split the korban of Gamliel. The yisroel completes the entire parsha, plus the first parsha of B’haalos’cha and finishes with”…kayn osso ess hamenorah.” (ShA 1 – Rama 1 – MB 4)
On Shabbos Chanuka remove two sifray Torah. With one, call up seven aliyos from parshas hashavua and say Kaddish. With the second sefer Torah, call up Maftir to read the nossi of the day. The maftir also reads “Ronni v’simchi”. If there is a second Shabbos Chanuka, the same procedure is followed – just the Haftara is from Melachim – about the nairos of Shlomo. (ShA 2 – MB 5,6)
If Rosh Chodesh Teves falls out on Shabbos remove 3 sifray Torah. With one, call up six aliyos to finish parshas hashavua. Place the second sefer Torah on the bima, then do hagba and gelila on the first. Open the second sefer Torah and read a seventh aliya for Rosh Chodesh – begin with “Oobayom hashabbos…” Place the third sefer Torah next to the second and say Kaddish. Then the maftir reads the nossi of the day from the third sefer Torah. The haftara is “Ronni v’simchi”. (ShA 3 – MB 9)
When Rosh Chodesh Teves falls on a weekday, remove two sifray Torah. From the first one read 3 aliyos. The cohen begins with the Tomid until “…reviis hahin” – levi until “…v’niskoh” – yisroel until “…v’niskoi”. From the second sefer Torah, call up one aliya – the nossi of the day. (ShA 3 – MB 12)