139:18 After Shabbos, one makes havdalah and then lights the Chanukah lights. (The Taz and many other authorities disagree with this, so one may light his menorah either before or havdalah at home – Mishnah Brurah 681:3.) In shul, we light before saying “V’yiten L’cha.”
139:19 If a person is not at home but is in another place, and he knows that his wife is lighting at home, he should light where he is, without the brachos. If possible, however, it would be preferable for him to first listen to the brachos recited by another person who is lighting there, responding Amen with the intention to fulfill his obligation with the other person’s brachos. After this, he should light without brachos. (He can also light for himself, with the brachos, by having specific intention not to be included in his wife’s lighting – MB 677:15.) If his wife is not lighting at home, he must light with the brachos.
The same is true of students boarding in someone’s home, though they might also partner with the head of the house by giving him a small coin for a share in the oil and the wicks. The head of the household should add a little oil beyond what he normally uses as their shares. However, they should best attempt to light for themselves. (All this only applies to students who provide their own food; if they eat at the host’s table, they are considered members of the household rather than guests – MB 677:1.) One who is in his own city but in another house should return home when it is time to light.