Gemara

(Mishnah - R. Akiva): If one was Makdish his property, and it includes matters proper for Korbanos Tzibur (i.e. Ketores), we give them to workers for their wages;

Ben Azai says, we may not do so. Rather, we separate wages for the workers [from Terumas ha'Lishkah, like in the previous Mishnah regarding excess Ketores. The wages become Chulin. We redeem [the matters proper for Korbanos Tzibur] onto the coins [separated] for the workers, and give [these matters] to the workers for their wages, and buy them back [from the workers] from the new Terumah.

Megilah 29a (Mishnah): When Rosh Chodesh Adar falls on Shabbos, we read Parashas Shekalim. If it falls during the week, we read it the previous Shabbos, and the next Shabbos has no special Parashah.

(Beraisa): When Rosh Chodesh Adar falls on Shabbos, we read Ki Tisa. The Haftorah is Yehoyada ha'Kohen.

29b (R. Yitzchak Nafcha): When Rosh Chodesh Adar falls on Shabbos, we take out three Sefrei Torah, in which we read the weekly Parashah, Musaf of Rosh Chodesh, and Parashas Shekalim.

Rishonim

Rosh (Megilah 4:10): The Yerushalmi says that it would be proper to read Parashas ha'Chodesh before Parshas Parah, for the first Parah Adumah was burned on Nisan 2. We read Parshas Parah first, for it is the Taharah of Yisrael.

Tosfos (Megilah 31a DH Maftir): (The Gemara says that on Shabbos Erev Rosh Chodesh, we read the Haftorah "Machar Chodesh.") Why don't we do so when Rosh Chodesh Adar or Rosh Chodesh Nisan is on Shabbos? This is because we read the Haftorah of Yehoyada ha'Kohen, which discusses Shekalim, and reminds people that Rosh Chodesh Adar will be that week.

Maharsha (on Tosfos): The Mordechai concludes that similarly, the Haftorah for Parshas ha'Chodesh proves that Rosh Chodesh Nisan will be that week. Tosfos' question is not clear to me. Why should Haftoras Machar Chodesh have precedence over Parshas Shekalim and Parshas ha'Chodesh, to override them? Also, why didn't Tosfos ask when Rosh Chodesh Adar or Rosh Chodesh Nisan is on Shabbos? We do not say the Haftorah of Rosh Chodesh then! I answer that in that case, the Haftorah of Parshas Shekalim or Parshas ha'Chodesh pertains to the last Keri'ah in the Torah, i.e. Parshas Shekalim or Parshas ha'Chodesh. However, every Erev Rosh Chodesh, Machar Chodesh does not pertain the last matter read in the Torah, and even so it overrides the Haftorah of Parshas ha'Shavu'a, which pertains to what was read. Therefore, there was a Hava Amina that it overrides also Parshas Shekalim and Parshas ha'Chodesh.

Maharil (Hilchos Teves, Shevat, Adar, 4, brought in Magen Avraham 685): In the four Parshiyos we do not mention the deceased (Kel Malei Rachamim), and we say (at Minchah) Tzidkascha... v'Tzidkascha.

Poskim

Shulchan Aruch (OC 685:1): If Rosh Chodesh of the Adar next to Nisan falls on Shabbos, we read Parshas Shekalim, which is Ki Sisa, until "v'Asisa Kiyor Nechoshes", and the Maftir "va'Yichros Yehoyada."

Mishnah Berurah (1): Chachamim enacted to read four Parshiyos from Rosh Chodesh Adar until Rosh Chodesh Nisan to commemorate four matters. Parshas Shekalim commemorates the Mitzvah of Machatzis ha'Shekel, which they had to give to the Lishkah every year for the Korban Tamid [and other Korbanos Tzibur]. The second is Parshas Zachor, to remember Ma'aseh Amalek. We read it the Shabbos before Purim, to put it close to the episode [with Haman,] who was from the seed of Amalek. Also, remembering [the Mitzvah of] wiping out Amalek should precede doing [the Mitzvos of Purim] - "veha'Yamim ha'Eleh Nizkarim v'Na'asim." The third is Parshas Parah Adumah, on the Shabbos before Parshas ha'Chodesh. In the Midbar, it was burned close to Nisan, in order to sprinkle [the water with] the ashes on Bnei Yisrael right after erecting the Mishkan, so they would be Tehorim and able to offer Pesach in its time. Therefore, we read this Parshah to pray to Hash-m that speedily He will throw also on us pure water! The fourth is Parshas ha'Chodesh, on the Shabbos next to Rosh Chodesh Nisan, for it says "ha'Chodesh ha'Zeh Lachem Rosh Chodoshim." This is not the primary Kidush. The primary Kidush is when the moon is seen and Beis Din is Mekadesh it. This Keri'ah is only mid'Rabanan.

Mishnah Berurah (2): It says "Zos Olas Chodesh b'Chodsho l'Chodshei ha'Shanah." "L'Chodshei" is extra. Rather, the Torah taught that there is a month that we must rejuvenate through bringing Olos, Temidim and Musafim from the new Terumah. We learn from a Gezeirah Shavah that this is Nisan. Therefore, we publicize about Shekalim earlier, in the Adar next to Nisan, so people will bring their Shekalim on [or before] Rosh Chodesh Nisan. We "pay bulls of our lips" through reading Parshas Ki Sisa, in which the matter of Shekalim is written. If they did not read the Parshah for that week, there is no compensation the next Shabbos.

Mishnah Berurah (3): We read this Haftorah, for it mentions donations to Bedek ha'Bayis. We do not read the Haftorah for Rosh Chodesh, even though it is Tadir (more frequent). Because we ended reading from the Torah with Parshas Shekalim, the Haftorah pertains to a similar matter.

Shulchan Aruch (ibid.): We remove three Sifrei Torah [from the Aron]. In one we read Parshas ha'Shavu'a, in the second we read [the Musaf] of Rosh Chodesh, and in the third we read Parshas Shekalim.

Kaf ha'Chayim (684:16): If they have only two Sifrei Torah, they read Parshas ha'Shavu'a in the first, [Musaf] Rosh Chodesh in the second, and what pertains to the day in the third.

Mishnah Berurah (4): Six read from Parshas ha'Shavu'a. Where the custom is to add to the Aliyos, we add.

Kaf ha'Chayim (684:17,18): Where the custom is to have a total of seven read from the Sefer Torah, five read from the first Sefer [and one each from the other two Seforim]. They do not say Kaddish until all seven read.

Mishnah Berurah (5): If after finishing Parshas ha'Shavu'a, they mistakenly took the Sefer Torah rolled to Parshas Shekalim, and he blessed and began reading, he finishes Parshas Shekalim, and reads Parshas [Musaf] Rosh Chodesh for Maftir, and for the Haftorah they read ha'Shamayim Kis'i (for Rosh Chodesh), since we ended reading from the Torah with Parshas Rosh Chodesh. The same applies on Rosh Chodesh Nisan if they mistakenly read Parshas ha'Chodesh before Parshas Rosh Chodesh.