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. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. One cannot pose questions from Tosafot's logic against the Rambam. Gavra aGavra KaRamit?!
9. The Rambam will rule like a Halacha found in the Sifrei if it's not contradicted by the Talmud.
10. The word Assur is used even when referring to Dinim MiDeoraita that would warrant Malkot.
11. 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.