Shulchan Aruch Chapter 682:
The Laws of the Al Hanissim (על הנסים) Prayer on Chanukah (3 Paragraphs)
Note:  The REMA is in Brackets [ ]

1.  On all 8 days of Chanukah we recite the Al Hanissim (על הנסים) prayer by Grace After Meals (before) the blessing on the land and in the Silent Prayer after the blessing of thanksgiving (מודים).  If you neglected to say it, you do not go back.  However, if you remembered in the middle of the (next) blessing before you spoke G-d's name, then you go back.  Even if you remembered between "blessed are thou" and "G-d" you should go back and recite it.  [There are those who state that if one forgets the Al Hanissim prayer by Grace After Meals, when one reaches The Merciful One (הרחמן) he should say "The Merciful One should perform miracles and wonders for us just like he performed them for our forefathers in those days (which was yet) in our time in the days of Mattisyahu etc." (הרחמן יעשה לנו נסים ונפלאות כשם שעשית לאבותינו בימים ההם בזמן הזה בימי מתתיהו ...)]

2.  On the Mussaf prayer of Shabbat and Rosh Chodesh it is necessary to mention Chanukah even though there is no Mussaf prayer for Chanukah.

3.  We do not say "just like you performed miracles ..." but we conclude with "and you performed for them miracles and mighty acts in those days at that time" [1].  The are are those who state that we do recite it.
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[1] The M.B. writes that the reason for this opinion is that the prayer is mostly talking about the past so we conclude with the past and not the present which is considered more like the future then the past.
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Shulchan Aruch Chapter 683:
No Title (1 Paragraph)

1.  All eight days of Chanukah we recite the complete Hallel (הלל) prayer. [All eight days of Chanukah we don't recite the Tachanoon prayer (תחנון) and Tzitkascha Tzedek (צדקתך צדק) or Lim'nat'zei'ach (למנצח) or Tzadook Hadin (??? צדוק הדין) even on the eve of Chanukah at the Minchah prayer.]

Shulchan Aruch Chapter 684:
The Order of the Torah Reading on Chanukah (3 Paragraphs)

1.  We read from the Torah the section listing the sacrifices that the leaders brought in the section (פרשה) of Na'sah (נשא) and we call three people up to the Torah on every week day in Chanukah.  We begin with "And it was on the day that Moses completed..." ויהי ביום כלות משה (Numbers 7:1) where we call up the Cohen (priest) [and such is our custom].  We call up a Cohen, a Levite and a Yisrael reading that which occurred on the first day (to Numbers 7:17).  [There are those who say that the Cohen reads everything until "on the first day" then the Levite and the Yisrael read from "on the first day" onward and such is our custom.]  On the second day, the Cohen starts reading from "on the second day" until "one young bull".  The Levite reads until "on the third day" and the Yisrael goes back and reads from "on the second day the same thing repeats itself on every day.  [There are those who state that the Yisrael reads starting from the next day.  In other words (on the second day the Yisreal reads) what occurred the third day.  They do the same thing on every day and such is our custom.]  On the eighth day we start reading from "on the eighth day" (Numbers 7:54) then conclude the entire section and continue reading from the first section of Be'hal'os'chah (בהעלותך) [and our custom is to conclude with "..so did they make the Menorah" (Numbers 8:4).]

2.  On Chanukah that falls out on Shabbat we bring out two Torahs.  On the first Torah we read from the section of the week and with the second Torah we read from the section of Chanukah.  We read the Maftir section "my joy and my gladness" (רני ושמחי).  If two Sabbaths fell out on Chanukah, on the second Shabbat we read Maftir within the section in Kings talking about the Candle Sticks of Solomon.  [And if Chanukah fell out on that Shabbat, we read the Maftir with the regular section of Chanukah.]

3.  If Rosh Chodesh (the new moon) in the Jewish month of Tevet fell out on the Shabbat of Chanukah, we bring out three Torahs.  We read from the first Torah six sections / aliyahs in the weekly portion.  We read from the second Torah one aliyah in the Rosh Chodesh portion beginning with "and on the Shabbat day".  From the third Torah we conclude with that which we normally read on Chanukah one Aliyah.  We read the Maftir of "my joy and my gladness" (רני ושמחי).  If Rosh Chodesh fell out on a weekday, we bring out two Torahs.  On the first Torah we read three aliyahs from the section of Rosh Chodesh.  With the second Torah we read from the section of Chanukah one aliyah.  If the Cantor made a mistake and read four aliyahs in the section of Rosh Chodesh, if they did not bring out the second Torah, they do not need to read any more.  However, if they already brought out a second Torah because of concerns that it appears like the second scroll is invalid we must read  from the second Torah a fifth aliyah within the section of Chanukah.  [If it is necessary to make a blessing over the portion of Rosh Chodesh, see Ch. 140.]

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