- Lift the cup with your right hand, pass it to your left hand and then place it back in your right hand lifting it three Tefach from the table. Recite until the end of the blessing of Hagafen while holding the cup in the right hand. Do not hold the Besamim while saying this.
- At the conclusion of the blessing of Hagafen, prior to the blessing of Besamim, place the cup down and hold the Besamim with the right hand. Then say the blessing.
- After smelling the Besamim place the Besamim down, and say the blessing of Meoreiy Haeish with nothing in the hands. Place both hands by the fire, first one’s palm and then one’s out fingers
- Prior to beginning the blessing of Hamavdil hold the cup in the right hand.
B. Ruling of Admur in Shulchan Aruch:
All items of which one is doing a Mitzvah with are to be held in one’s right hand. Therefore the following is the order of Havdala. One is to hold the cup of wine in his right hand and the Besamim in his left hand, [while reciting Hinei Keil Yeshuasi and] the blessing of Borei Peri Hagafen. When he reaches the blessing of Besamim he is to switch the cup to his left hand and take the Besamim in his right hand and say the blessing. Likewise for the blessing of Meorei Haeish it is best to continue holding the cup in his left hand so he can place his right hand by the fire.  Afterwards he is to transfer the cup back into his right hand and recite the blessing of Hamavdil.
C. Ruling of Admur in Siddur:
When one reaches the blessing of Besamim he is to hold the cup in his left hand and take the Besamim in his right hand and say the blessing. For the blessing of Meorei Haeish one is to switch the cup back to his right hand. [One then places the cup down or into his left hand] and looks at the nails [of his right hand]. Afterwards one transfers the cup back into his right hand and recites the blessing of Hamavdil.
How is a lefty to hold onto the Havdala cup?
 As witnessed by thousands of Chassidim in public on various occasions, and as can be viewed from recorded footage.
 This custom is prolific amongst Chabad as well as other circles. See Piskeiy Teshuvos 296/15 that the world is no longer careful to follow the order written in Shulchan Aruch. Ashel Avraham Butchacher did not originally follow the custom brought in Shulchan Aruch, although later changed his custom.
As for why the custom today has changed from the custom written in Shulchan Aruch-See Lehoros Nasan 8/17
 This matter was also omitted in the Siddur. [Ketzos Hashulchan 96 footnote 4]
 Rama 298/3
 This follows the ruling of the Mordechaiy, brought in Kaf Hachaim 298/21; See Shaar Hakolel 32/3.
 Ketzos Hashulchan 96/2 gives both options and so also learns Kitzur Halachos 296 footnote 11; However Shaar Hakolel 32/3 and Kaf Hachaim ibid brings to place the cup in the left hand while using the right hand to place near the flame.
 Ketzos Hashulchan 96/2
 Based on Admur 183/7; 651/14; Tzemach Tzedek Orach Chaim 5/8 regarding Netilas Yadayim
 So is the ruling based on Kabala that one always follows the general right hand of the world. [Kaf Hachaim 183/20]