The Shulhan Aruch (Orah Haim 299) writes that even after dark on Mosa’eh Shabbat, it is forbidden to perform Melacha until one recites Habdala. He adds, however, that "Habdala" in this case refers not only to the Habdala which we recite over a cup of wine, but also to the "Ata Honantanu" paragraph which we add in the Arbit service on Mosa’eh Shabbat. Therefore, one may perform Melacha on Mosa’eh Shabbat after reciting the Amida of Arbit with "Ata Honantanu." Moreover, the Shulhan Aruch writes, even if somebody recited the words, "Baruch Ha’mabdil Ben Kodesh Le’hol," this suffices as a "Habdala" which allows performing Melacha. Thus, for example, the Habdala candle may be lit before Habdala, since one has already recited either "Ata Honantanu" in Arbit or the words "Baruch Ha’mabdil Ben Kodesh Le’hol." But before one recites "Ata Honantanu" in Arbit or "Baruch Ha’mabdil," he may not perform Melacha, even though night has fallen.
Many women do not recite Arbit, and on Mosa’eh Shabbat they want to perform Melacha – such as make a phone call – while they wait for their husbands to return from the synagogue. Some mistakenly assume that once the time written in the calendar has passed, they are now permitted to perform Melacha. It is important for them to know that Melacha is permitted at this point only after they recite, "Baruch Ha’mabdil Ben Kodesh Le’hol."
It should be noted that some Rishonim – specifically, the Rosh and the Rif – maintained that it does not suffice to recite "Baruch Ha’mabdil Ben Kodesh Le’hol" to permit performing Melacha after Shabbat. In their view, one must recite a complete Beracha: "Baruch Ata Hashem Elokenu Melech Ha’olam Ha’mabdil Ben Kodesh Le’hol." The Shulhan Aruch does not accept this ruling, and instead prefers the view of Rashi, that reciting the words "Baruch Ha’mabdil Ben Kodesh Le’hol" suffices, as mentioned. Although we follow the Shulhan Aruch’s lenient ruling, nevertheless, Hacham Bension Abba Shaul (Israel, 1923-1998) writes that one who wishes to be stringent should not perform any activity forbidden on Shabbat on the level of Torah prohibition until the recitation of Habdala over a cup of wine.
It is customary to blow the Shofar at the conclusion of the Yom Kippur service, even though Yom Kippur has not yet ended. (The Shofar blowing usually takes place some 15-20 minutes or so after sundown, which is clearly before the end of Yom Kippur.) The Halachic authorities write that this is permissible because Shofar blowing is not strictly forbidden on Yom Kippur, certainly not on the level of Torah prohibition. Therefore, although we do not generally permit blowing a Shofar on Shabbat or Yom Tob, it is allowed at the end of Yom Kippur, as it serves the purpose of a Misva.
Summary: Once night falls and Shabbat has ended, it is still forbidden to perform Melacha until one either recites "Ata Honantanu" in the Amida of Arbit, recites the complete Habdala over a cup of wine, or recites the words "Baruch Ha’mabdil Ben Kodesh Le’hol." Some, however, wait until Habdala is recited over a cup of wine before engaging in activities forbidden on Shabbat on the level of Torah prohibition, in order to satisfy all opinions.