This article is an excerpt from our Sefer
Buy me here or on Amazon.com
Wishing each other a sweet new year:
We begin to wish each other a “Kesiva Vachasima Tovah” starting from Rosh Chodesh Elul. [Some are accustomed to begin doing so from the 15th of Menachem Av.] In a letter to a friend one must begin [or end] with a blessing for the person to have a good year. [The Rebbe’s custom was to write the blessing at the end of the letter. One is to continue to do so until Rosh Hashanah. From after Rosh Hashanah until Yom Kippur one writes Chasima Vegmar Chasima Tovah. From after Yom Kippur it is no longer our custom to write the blessing, although some do so until Hoshanah Raba. ]
Sparks of Chassidus
The blessing affects oneself and the person being blessed:
The reason of blessing each other is because the words of a Jew have power and affect. One can actually change another Jew’s future through a kind blessing. When one blesses another Jew this adds to the blessing of Hashem to every single Jew in Klal Yisrael in both physical and spiritual matters.
Going out of one’s way to bless each other: 
For the above reason each person is to actually go out of his way to bless a fellow Jew with a Kesiva Vechasima Tova both orally and in writing. A man is to bless another man and a woman another woman. Children are to bless other children of their gender, boys are to bless other boys and girls are to bless other girls.
Story of Rebbetzin Devorah Leah:
In the known story of Mesirus Nefesh that the daughter of the Alter Rebbe took upon herself to exchange her life for the life of her father who was given a supernal decree of death, the blessing of “Kesiva Vechasima Tova” took a pivotal role. It was understood that whoever would be the first to wish the other this blessing on Rosh Hashanah would take the decree upon himself and revoke the decree from the person who received the blessing. On that first night of Rosh Hashanah against the usual practice of the Alter Rebbe viewed in previous years to avoid speaking at all on Rosh Hashanah, the Alter Rebbe asked for his daughter Devorah Leah. The Alter Rebbe came to approach his daughter Rebbetzin Devorah Leah and began blessing her with “Leshana..”. Before he got a chance to finish the blessing his daughter cut him off and said “Leshana Tova Tekaseiv Vesechaseim, Father don’t speak”. And so it was that she exchanged her life for the life of her father and saved the Chassidic movement. She fell sick the next day and passed away on Tzom Gedalia.
 Maharil brought in Beir Heiytiv 581/10; Kitzur Shulchan Aruch 128/2; Kaf Hachaim 581/18; Regarding wishing each other a good year orally see Hisvadyos 1988 Vol. 4 p. 209
 “You shall be written in and sealed for a good year”. This is hinted to in the words “Vayishalu Ish Lireieihu Leshalom” which is also an acronym for Elul [Lekutei Mahrich]
 Custom to begin from the 15th of Av: The Shaar Yisacher and Darkei Chaim Veshalom [684; Munkatch] write that one is to begin wishing each other Leshana Tova starting from the 15th of Av. The Rebbe states that it is a Minhag Yisrael to do so. [Hisvadyos 1991 Vol. 4 p. 179; printed in Shulchan Menachem 3/72] The Gematria of “Chamisha Asar Beav” is the same as “Kesiva Vechasima Tova”. [Darkei Chaim Veshalom ibid; Hisvadyus ibid] This is also hinted to in the acronym for the Mazal of Menachem Av which is “Aryeh” and stands for Elul; R”H; Yom Kippur; Hoshanah Raba, as in the month of Av is hinted to the completion of the Piska Tova of Hoshanah Raba. [Rebbe ibid] This blessing is found in letters of the Rebbe Rayatz and Rebbe written in the month of Menachem Av. [Otzer p. 11-13]
 Some Poskim write that the blessing is to be written in the beginning of the letter. [Beir Heiytiv ibid; Elya Raba 581/1; Drashos Maharil; Kaf Hachaim 581/18] Others mention that the blessing may be written either in the beginning or end of the letter. [Mateh Efraim 581/9; Likkutei Mahrich in name of Avodas Hageirshony]
 Mahril brought in Beir Heiytiv 581/10; Kitzur Shulchan Aruch 128/2; Kaf Hachaim 581/18
 As is seen in hundreds of letters printed in Igros Kodesh. So was also the custom of the Rebbe Rayatz. [Otzer Minhagei Chabad p. 11] See Otzer p. 10 for the Nussach used by the Tzemach Tzedek and Admur Maharash and Rashab. They wrote in the beginning of the letter, although at times the Rebbe Rashab wrote it at the end of the letter. It is not found in the letters of the Mittler Rebbe or Alter Rebbe, and there are letters of the Rebbe Rayatz in which no blessing is written.
Writing to a gentile: See Shulchan Menachem 3/72 footnote 1 that the Rebbe once told the secretary to write this Nussach to a gentile, stating that also the gentiles are judged on this day.
 So is the wording of the Rebbe on many letters written during Aseres Yimei Teshuvah.
 The Rebbe omits the blessing in letters written after Yom Kippur. This follows our custom brought in Sefer Haminhagim [p. 146 English edition] from the Friediker Rebbe [Sefer Hasichos 1948 Sichas Hoshanah Raba] that we do not say Gmar Chasima Tovah or Piska Tova on Hoshana Raba. However there were letters of the Rebbe Rashab and Rebbe Rayatz of after Yom Kippur that the blessing is found. [See Otzer Minhagei Chabad p. 10-11]
 See Piskeiy Teshuvos 581/1 footnote 7
 Sichas 1st Elul 1988
 Sichas 1st Elul 1988
 The custom is for also boys before Bar Mitzvah to bless adults even though this is not so much Derech Eretz. [Hisvadyos 1988 4/339]
 Based on Likkutei Dibburim Volume 1 Likut 2 [p. 56-60 in Hebrew addition]
 See Otzer Sipurei Chabad Volume 3 p. 265