The Shabbat after Simchat Torah is Shabbat Bereishit -- "Shabbat of Beginning" -- the first Shabbat of the annual Torah reading cycle, on which the Torah section of Bereishit ("In the Beginning") is read.
The weekly Torah reading is what defines the Jewish week, serving as the guide and point of reference for the week's events, deeds and decisions; Rabbi Schneur Zalman of Liadi called this "living with the times." Hence the theme and tone of this week is one of beginning and renewal, as we launch into yet another cycle of Torah life. The Rebbes of Chabad would say: "As one establishes oneself on Shabbat Bereishit, so goes the rest of the year."
Link: Beginnings
This Shabbat is Shabbat Mevarchim (“the Shabbat that blesses" the new month): a special prayer is recited blessing the Rosh Chodesh ("Head of the Month") of the upcoming month of Cheshvan (also known as "MarCheshvan"), which falls on Wednesday and Thursday of next week.
Prior to the blessing, we announce the precise time of the molad, the "birth" of the new moon. See molad times.
It is a Chabad custom to recite the entire book of Psalms before morning prayers, and to conduct farbrengens (chassidic gatherings) in the course of the Shabbat.
Links: Shabbat Mevarchim; Tehillim (the Book of Psalms); The Farbrengen