Shulchan Aruch Chapter 676:
The Order of the Blessings and the Lighting (5 Paragraphs)
Note: REMA in Brackets [ ]

1.  When we light on the first night, we recite three blessings: "... to light the Chanukah candles" (להדליק נר של חנוכה), "... who performed miracles for our forefathers ..." (שעשה נסים), and "... who kept us alive ..." (שהחיינו).  If you did not recite the blessings on the first night, you may recite them on the second night or whatever night you remember.

2.  After the first night, you recite two blessings: "... to light the Chanukah candles" (להדליק נר של חנוכה), and "... who performed miracles for our forefathers ..." (שעשה נסים).  [You should recite all the blessings before you begin to light.] 

3.  Consider the case where one did not light the Chanukah candles and in the future one is not going to light on that night, even in his household.  When he sees Chanukah candles he should recite the blessing  "... who performed miracles for our forefathers ..." (שעשה נסים) and on the first night he should also recite the blessing of "... who kept us alive ..." (שהחיינו).  If afterwards on the second or third night he lights the Chanukah candles, he does not repeat the blessing of "... who kept us alive ..."שהחיינו

4.  After you light the candles, you say "these candles we light on the deliverances, on the miracles and on the wonders that you performed..הנרות הללו אנו מדליקין ".

5.  One should begin the lighting on the first night by placing the first candle on the right most side.  On the second night when one adds another candle next to it, one should start the lighting starting from the left in order to turn to the right.  The same applies on the third night.  When one adds another candle near the first two, he begins lighting from the added candle and afterwards he turns (his attention) to the right side.  Similarly, after every night one always makes the blessing first on the extra candle that one adds to the Menorah (for that night). On the later nights, the Menorah gets fuller.  

Shulchan Aruch Chapter 677:
The Law of a Guest on Chanukah (4 Paragraphs)
Note: REMA in Brackets [ ]

1.  A guest who does not light Chanukah candles in his own house must give a penny (פרוטה) to the host of the home he is staying in to partner with him in the ownership of the oil used for the Chanukah lamps.  If the room he dwells in has a doorway (outside) that is open to him, he must light at that doorway even though that this house is not his real residence but he merely sleeps there and eats at the table of his host (1).  The same applies to a son who eats by his father.  [Some say that in our time where we actually light indoors, he should light in the place where he eats and such is our custom.]

2.  A child who reached the age of teaching must light Chanukah candles.

3.  There are those who state that even if one will light Chanukah candles in his home, if he now is an location where there are no Jews, he lights there with all the blessings. [For one is obligated to see the candles and such is our custom even if he is next to Jews and the candles are visible.  If one wishes to be strict and to light a second time for himself, he lights and makes a blessing over them and such is our custom (2).]

4.  If one has leftover oil on the eighth night that was included in the amount needed for lighting, one should make it into a torch and burn it by itself.  The reason is that the oil was set aside for the Mitzvah (3) .  If it became mixed with other oil and was not diluted by a factor of sixty to one, there are those who state that one does not need to dilute it. (4)
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(1) The M.B. states that the reason is that he may forget to light Chanukah candles
(2)  He is speaking about a case when he lit once for all the members of his household but did not have himself in mind so he can light a second time only for himself.
(3)  The oil is holy since it was set aside for the Mitzvah of Chanukah and can not be used for another purpose.
(4)  M.B: Some say that Rabbinically prohibited items are permitted if they become mixed with something else.
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