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 Elul, which falls on Thursday and Friday of next week.
As noted a here, this day is especially significant since this is the final (and culminating) such blessing of the year.
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
In preparation for the festival of Shavuot, we study one of the six chapters of the Talmud's Ethics of the Fathers ("Avot") on the afternoon of each of the six Shabbatot between Passover and Shavuot; this week we study Chapter Five. (In many communities -- and such is the Chabad custom -- the study cycle is repeated through the summer, until the Shabbat before Rosh Hashanah.)
Within every love, there is fear: The fear of separation from that which you love.
A child fears separation from her parents, a lover from his beloved, the body fears separation from the soul, and the soul from its Source Above.
So what do you love? Look at your worries and you will know. If you seethe in worry over your debts and financial future, then it is the material world you love—because you believe in the material world and you see it as the source of all good.
If you sit and fret over the comments of others and the glances they throw at you, then it is social acceptance that you love, that you have made into your god.
Cleave to the Source of Life and your heart will have no room for fear of this world.