Klalei HaPsak (Halachic Decision Making)

Geonim

1. The term "Geonim" generally refers to those who lived between the Savoraim and the Rif, though the institution of Geonim did extend beyond then. Some say that the term Gaon is short for "Rosh Yeshivat Gaon Yaakov," while others claim it was reserved for those who were experts in all sixty Masechtot of Shas, corresponding to the Gematria of גאון.
2. The monograph on Hilchot Tefillin from the times of the Geonim is claimed by some to be super authoritative, as "the words of the Geonim are tradition" (דבריהם דברי קבלה) in that they had access to the first edition of Talmud Bavli, which was clearer than ours. At the same time, a number of Rishonim poke holes in the work and argue it shouldn't be followed when it contradicts Talmud Bavli.

Rambam

1. The Maharashdam (analogous to the Radbaz and the Rif) believes that since the Rambam saw the other opinions on each issue and still decided the way we did, we should follow his rulings. On the other hand, a number of Ashkenazi authorities feel that the Rambam is a minority in the face of the Baalei HaTosafot.
2. When a contradiction is found between the Perush HaMishnayot and the Mishneh Torah, the Halacha follows Mishneh Torah, which was written later and as a set of rulings, not a set of elucidations of the Mishnah.
3. In Mishneh Torah, the Rambam focuses on relaying rulings explicated in the Gemara in a lucid way, while leaving out rulings that can only be inferred but aren't stated explicitly.
4. Every word of the Rambam is written with tremendous precision and exactness, enough for one to infer from his words as one would from the Gemara itself. Similarly, the Maharalbach warns that one shouldn't rush to reject the Rambam for coming off as against the Gemara, but should rather pin the in-congruence on our own lack of understanding.
5. It is not uncommon for the Rambam to pin a ruling on a Pasuk not mentioned in or even rejected by the Gemara, because he felt it to be simpler or more acceptable, especially if there's no practical difference.
6. One cannot infer from the presentation of a ruling in one section of Mishneh Torah and its absence in another seemingly appropriate section that it only applies in one and not the other, as the Rambam's goal is to present the Talmud's rulings in their wording in their appropriate place. For example, a Halacha in Terumot that might also fit in Maachalot Assurot cannot be assumed to only apply in Terumot and not Maachalot Assurot given its presence in the former and absence in the latter. This is, however, a valid tool in reading other Poskim, such as the Tur.
7. Though the Rambam never relies in Mishneh Torah on what he already wrote in Peirush HaMishnayot, he does rely on what he wrote in earlier sections of Mishneh Torah, and perhaps even later ones.
8. The focus of Sefer HaMitzvot is not to determine which Mitzvot are part of the 613, not to present a comprehensive of accurate representation of their Halachot and details. Therefore, when studying Sefer HaMitzvot, questioning the count of Mitzvot is wholly acceptable, but questioning the details of the Mitzvot is not. The Mishneh Torah was written to address those details, and, even if there are distinct differences, it's always possible that he changed his mind over time.
9. The term "MiDivrei Sofrim" can refer to Dinim MiDeRabbanan, as well as any Din MiDeoraita not stated explicitly in the Torah, such as one derived via the thirteen Middot, because without the Chachamim it would not be understood.
10. One cannot pose questions from Tosafot's logic against the Rambam. Gavra aGavra KaRamit?!
11. The Rivash argues that the Rambam will refer to a Takkanat Chachamim as "Torah," such as in "Lo Hikpida Torah" in reference to the Ne'emanut of an Ed Echad, while others disagree.
12. Sometimes our translation of Perush HaMishnayot will refer to a din as being MiDeRabbanan, but it's probably just a mistaken translation of "MiDivrei Sofrim."
13. Consistently marking each Din as a Gezeirah or Halacha LeMoshe MiSinai is not a priority for the Rambam: sometime he mentions the Din's classification, while other times he does not.
14. The Rambam will rule like a Halacha found in the Sifrei if it's not contradicted by the Talmud.
15. The word Assur is used even when referring to Dinim MiDeoraita that would warrant Malkot.
16. When the Gemara presents more specific arguments predicated on accepting one of two possible assumptions - "Im Timtzi Lomar" - the Geonim and Rambam understand that the Halacha assumes like that assumption. Some say this is only true if the Gemara did not leave the very same uncertainty pending with a "Tiku" elsewhere, while others argue the opposite. The two levels of the Im Timtzi Lomar cannot be interchangeable, meaning if assuming A over B and then asking C over D is equivalent to assuming C over D and then asking A over B, this rule does not apply for the Rambam. The words must also be explicit in the text of the Gemara, so two subsequent questions, one building on the previous, would not be subject to this rule. The Poskim dispute if this is only true when the Amora in the Gemara himself uses these words to navigate the situation or if it's even true when the omniscient narrator of the Sugya does so externally of the Amora's words.
17. The Rivash and Rosh warn that one who attempts to rule on practical matters solely from Mishneh Torah without understanding its Talmudic context will likely mistake Assur for Muttar and Muttar for Assur, thinking he understands the material. At the same time, the Rambam's explicit intention was to write the Halacha so clearly that one need not be bogged down by the confusing Sugya and need only Mishneh Torah to know how to act, so some Acharonim, such as the Ohr HaChaim and Baal HaTanya are less concerned. While that is true, the Rambam himself explains in a letter that he did so for people for whom understanding the Gemara was beyond their reach.
18. The Ramban did not have the Introduction to Perush HaMishnayot available to him, as Hebrew translations of the Arabic were not yet available in Spain, according to the Yad Malachi, who posits that had they been available, the Ramban would not have been as quick to argue.
19. In Mishneh Torah, the Rambam's style is to write only what it says in the Gemara and not the interpretation, but his intention is to for the interpretation of the Gemara to be applied to his words, as well, though some disagree.
20. Seldom does the Rambam disagree with the Rif, so one should not assume so unless there are already a great number of Rishonim for him to side with.
21. If the Gemara presents two opposite understandings and then rejects on, the Rambam will formulate it in a way that accepts the accepted one and implies the rejection of the rejected one.

Further Reading

• Yad Malachi, especially the Machon Yerushalayim annotated edition
• Ein Yitzchak, by Rav Yitzchak Yosef
• Orot HaTahorah, by Rav Zecharia Ben Shlomo