How are the sephardim nohag when it comes to Motzei Shabbos Channukah, do they make havdallah first or light neros channukah first?
The Sephardi custom in shul is to light Chanukah candles first, and then to make havdallah (Shulchan Aruch 681:2).
At home, although the Rema writes that Chanukah candles are lit first, many write that havdallah is made first, and Chanukah candles are lit after havdallah (as ruled by the Pri Megadim (1), Taz (1), Pri Chadash).
The Mishnah Berurah (3) writes that both options are viable; in particular, where havdally is not made in shul, the ruling of the Rema will not apply.
Concerning the Sephardi custom, see Birchei Yosef (681:1), who mentions both options as different customs. It appears that the more common custom is to make havdalah first, but as the Birchei Yosef and others write, both options are possible.