On Motzai Shabbat - the 4th night of Chanukah this year - one first makes Havdalah and then lights the Chanukah Menorah.
In Shul the Menorah is lit after the full-Kaddish - before וְיִתֶּן לְךָ - on Motzai Shabbat.
Source: Kitzur Shulchan Aruch 139:18
Some have the custom of lighting the Menorah before making Havdala, since one already heard Havdalah in shul. (Source: רמ"א 581:2)
The Haftara this week is the Chanuka one (רָנִּי וְשִׂמְחִי בַּת צִיּוֹן from Zecharia 2:14)..
Shabbat Shalom uMevorach, Rosh Chodesh will be on Tuesday and Wednesday.
Thursday, 25 Kislev 5774
On weekdays, the preferred time is at sunset (16:40) or nightfall (17:10) depending on family custom.
You can light any time after this - but you cannot make the Brachot then, unless somebody else is awake in the house with you - or you live on a busy street and people are still walking outside and they can see your Chanuka Menora.
The latest time to light would be 4:15 the next morning - 30 minutes before dawn.
Once it's time to light the Menora, one should not do anything else except get organized to light. Even learning Torah and eating is not allowed; though one can have a light snack (fruit or similar).
The only exception is: one can first Daven Maariv - תפילת ערבית - if one lights at nightfall.
After candle lighting one can do anything. However, there is an ancient custom that women do not do any work for the first 30 minutes, to commemorate their pivotal role in the Chanuka victory. ("Work" being anything they cannot do on Yom Tov.)
The custom is to spend these 30 minutes singing Maoz Tzur and other Chanuka songs, relating the story of Chanuka and discussing the Halachot of Chanuka.
On Friday afternoon one lights Shabbat candles at the usual time (16:00) and one has to light the Menora BEFORE lighting Shabbat candles. (So the Menora has to be lit between 15:30 and 16:00)
The Menora has to burn until 30 minutes after dark - so you'll need oil or candles that will last for at least 70 minutes.
Since you cannot move the Menora on Shabbat, you have to place it in a safe place - but (if possible) it should not be near your Shabbat candles.
On Motzai Shabbat you must wait until Shabbat is over (17:15) and then you make Havdala and light the Menora. Which to do first depends on family custom.