The Torah portion is Tazria, Leviticus 12:1-13:59.This parshah speaks of ritual purity and offerings made in various medical situations: a woman after childbirth and a skin condition called tzara'at (often translated as leprosy, but it is clearly something else as it also affects clothes and buildings). It discusses the temporary period of ritual impurity, the offerings made and the treatment of tzara'at. The commandment of circumcision also appears in this portion.
There is a special seventh aliyah (7th piece of the Torah reading) for Rosh Chodesh Shabbat: Numbers 28:9-15. This portion lays out the offerings made on Rosh Chodesh (the beginning of the new month) when it occurs on a Shabbat.
There is a special maftir portion (the final piece of the Torah reading) for Shabbat Ha-Chodesh: Exodus 12:1-20. Identifies "this month," the month of the Exodus now known as Nissan, as the first month of the year and speaks of the Pesach offering and the coming Plague of the Firstborn and the festival of Pesach (Passover).
The haftarah is for Shabbat Ha-Chodesh, Ezekiel 45:16-46:18. Speaks of the offerings and preparations for Pesach (Passover), which is coming soon!
In synagogues using the Sephardic tradition, the Haftarah is Ezekiel 45:16-46:15.