The Shulhan Aruch (Orah Haim 342) establishes the rule that during the period of Ben Ha’shemashot – the 13.5 minutes after sundown – at the beginning of Shabbat, one is allowed to perform actions which are forbidden on Shabbat only Mi’de’rabbanan (by Rabbinic enactment). Although the Shabbat prohibitions take effect immediately at sundown, actions which the Sages forbade on Shabbat may be performed during the 13.5-minute period of Ben Ha’shemashot.
This applies during Ben Ha’shemashot both at the beginning of Shabbat, and at the end of Shabbat, meaning, for 13.5 minutes after sundown on Shabbat afternoon.
An example of this Halacha is moving Mukseh. Since moving Mukseh is forbidden on Shabbat Mi’de’rabbanan, it may be done when necessary during Ben Ha’shemashot. Likewise, one may ask a non-Jew during Ben Ha’shemashot to turn on a light or perform another action that is forbidden for a Jew on Shabbat. Asking a non-Jew on Shabbat to perform an action forbidden for Jews on Shabbat is prohibited Mi’de’rabbanan, and so this is allowed when necessary during the period of Ben Ha’shemashot.
Another example is separating Ma’aserot (tithes) from produce on Shabbat. Separating tithes is forbidden on Shabbat Mi’de’rabbanan, and so it is allowed during Ben Ha’shemashot if one needs this food for Shabbat.
However, the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) notes that there are several exceptions to this rule. For example, one may not carry an object in a public domain during Ben Ha’shemashot a distance less than four Amot – even though carrying this short distance is forbidden only Mi’de’rabbanan. Since this can easily lead to a Torah violation, the Sages did not permit this during Ben Ha’shemashot. Likewise, one may not throw an object from a public domain into a private domain during Ben Ha’shemashot. Another exception is a "Melacha She’ena Sericha Le’gufah" – a forbidden action performed on Shabbat for a different purpose than the purpose for which this Melacha (forbidden action) is normally done. (The classic example is digging in the ground not for the purpose of making a ditch, but one needs the earth.) Such an action is not allowed during Ben Ha’shemashot.
Additionally, Hacham Ovadia Yosef ruled that one may not perform an action with a "Shinui" – in an unusual way – during Ben Ha’shemashot. An example would be writing with one’s left hand. Although performing a Melacha in this manner is forbidden only Mi’de’rabbanan, this is not allowed during Ben Ha’shemashot.
Moreover, performing an action that is forbidden Mi’de’rabbanan during Ben Ha’shemashot applies only in situations of dire need, or for the purpose of a Misva. Examples include one who needs to tithe food in order to have food for Shabbat, as discussed, or if a light is needed in the room for the Shabbat meal or some other Misva. If there is no dire need and no Misva for which the action is required, then this is not allowed.
Summary: As a general rule, actions forbidden on Shabbat by Rabbinic enactment are allowed during the 13.5-minute period after sundown when Shabbat begins and at the close of Shabbat, if there is some dire need or for the purpose of a Misva. Examples include asking a non-Jew to perform an action that is forbidden for Jews on Shabbat, like turning on a light, or moving Mukseh. There are, however, exceptions to this rule, and thus, for example, one may not perform a Melacha in an unusual manner (such as with one’s left hand) during Ben Ha’shemashot, even though this is forbidden by force of Rabbinic enactment.