The Torah portion is Noach, Genesis 6:9-11:32. In synagogues using the Triennial system, 5785 is year 3 and the Torah reading is Genesis 11:1-11:32.
This portion covers a large swath of early history, from Noah and the Flood to the arrival of Abraham and his family in Canaan.There is a special maftir portion (the final 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.
The haftarah is for Rosh Chodesh, Isaiah 66:1-24. This portion speaks of the many sins committed by the People in Isaiah's time and the consequences, but promises that some will prosper and endure.