Before I begin, remember, this is used for BASES, not nucleophilicity. (i.e. Bronsted Bases, not Lewis Bases, although trends are usually similiar)
C-Charge
In order to rank bases, you look at charge first, the more negative it is, the more basic. I.E. O^-2,OH-, H2O.
A- Atom
The key here is to realize what basicitiy is; the ability of a base to ACCEPT a proton. In other words, the more stable the base, the less likely it is to accept a proton. For atom, you want to look at two things: the electronnegativity and the size of the atom. Lets think about it: the more EN an atom, the more its ability to hold electrons in a bond. That ALSO means it is more willing to hold on a negative charge as an ion. In other words, the more EN an atom, the less basic it is bc it is MORE STABLE, or it is happy with the negative charge. The EN rule for an atom is used when looking at the same period.
I.E. C->N->O->F- in Period 2.
The next rule for atom is the SIZE. This is generally done looking down a column. The larger the ion, the more stable it is (not really, but for the DAT that is what you need to know), and the LESS basic it will be bc it is more stable. So looking at OH- and SH-, SH- is more stable, and is thus a weaker base, and OH- is a stronger base (since S is larger than O).
R- Resonance
This is simple. If you can draw resonance structure vs. not draw them, the more resonance stabilized speciies will be less basic bc it is MORE STABLE. The key here is charge dispersal (as is the same with DIPOLE INDUCTION, for the "DI" in CARDIO). THe more dispersed the charge, (i.e. the more resonance forms there are), the more stable the species.
DI- Dipole Induction
Once again, here, we are looking at stability based on the species ability to disperse CHARGE. If we have a negatively charged species, something that can take that negative charge and remove it from its isolated atom will stabilize the species. So we need Electron Withdrawing Groups; what is an EWG? EWG are generally positively charged species (i.e. a carbon bonded to 3 Fluorines or a Nitro-group--which is the strongest EWG). They withdraw electrons bc they are electron DEFICIENT, as indicated by their + charge. This pull on electrons will pull electrons from the nearest atom, which will now also be positively charged. This atom will also then will pull electrons from its nearest neighbor, causing a chainreaction as electrons are pulled towards the electropositive atom. THe key here is distance, the closer the EWG to the negative charge, the more it stabilizes the species.
O-Orbitals:
Remember, when bonds formed, the orbitals are generally hybridized, and certainly is the case for Carbon. If the electrons are located closer to the nucleus, they are more stable. In terms of closness to the nucleus, rembmer, the s orbital is closer. If the orbital has more s character, that means the electrons are also closer to the nucleus, and the elctrons will be more stabilized. Therefore, we have sp>sp2>sp3 in terms of stability, and the less basic it will be. So..., an acetylide ion is more stable than a negatively charged alkene, whichs is more stable than a negatively charged alkane, and thus basicity will decrease (i.e. from least basic to most basic, acetylide ion<alkene ion<alkane ion).
In order to rank acids, we just look at the conjugate base and determine its STABILITY w CARDIO. This requires some thinking, but take your time and make sure you understand it (it will appear on your DAT). A good way to understand this is to realize that the more stable the base, the MORE THE BASE IS FAVORED, and the acid IS MORE ACIDIC TO FORM THE BASE! I.E., at equilibrium, the acid will dissociate to form the stable base.
Stable=weaker base bc it does not want to accept a proton bc IT IS HAPPY THE WAY IT IS.
I know this is sounds so confusing. But do not panick, just think it out. After reading this, explain it yourself in your head and make sure you understand it.
There are some exceptions. Two to note are (as also stated in Chad's Videos):
Ammonium Ion vs Carboxylic Acid (pka10 vs pka 4, respectively)
and
Amines vs. Terminal Alkynes (pka 33 vs 25, respectively).
