I'm gonna give basic results of Crystal Field and related VBT, and I don't think the generalizations made on shape are good in that ppt like Ni+4 Co+3 etc..
Assumptions
1.Electrostatic interaction only between ligand's dipole or charge and positive charge of central metal ion
2.Ligands are point charges

(source: pgcc.edu)

Look up shape of an octahedral, x,y,z axes passing through vertices and central metal at its centre, ligands approach along this axis and increase the energy those orbitals which are along axes which are dx2-y2 and dz2 due to electronic repulsion

so, we have 3 "d" degenerate {equal energy} of one level of energy and two of a higher level, now FILL the orbitals {from start if you want to but just the d subshell is fine} by paulli,hund's rule . When there are 3 unpaired electron in lower energy level, its about to happen, if the energy gap between the levels {increases with strength of field of ligand, look up spectrochemical series for strength [chelating ligands have extra stability and need to be taken care of properly, their strength is more than specified in order as that order doesn't take ring formation entropy increase into consideration [if we made 2 ammonias into ethylene diammine, reaction's products are more so entropy increases and free energy becomes more negative]]} is more than energy needed to piss off hund (pair the electrons) then, pairing will start until the 3 orbitals have 6 electrons, now the next batch starts and start filling like you would normally do, when it's done, start to count orbitals left with no electrons with are lowest in energy and they (6 of them) hybridise to 6 equal energy orbital and as my comment said, each coordinate bond fills one orbital so, we needed 6 orbitals
things are a little complicated for tetrahedral and square planar with the energy gaps not really as simple as described above {to this day i can't convince myself of dz2 in square planar} so, just google it and learn it , and try to derive it by the same method as before
When we write d before, it means inner orbital d orbital is used ex- 3d for Fe+3
and when after one means 4d for Fe+3 i.e. the next shell's d
- Always start with coordination number i.e. number of ligands
[Any one wants to make inner orbital complex as shorter and better bonds]
When it's
4 - Tetrahedral {sp3}[only if we don't get an empty d orbital left , even by hook or crook] or Square Planar {dsp2}
5(rare) - Triagonal Bipyamidal {sp3d} and {dsp3}
6 - octahedral {sp3d2} or {d2sp3} with same logic, latter being preferred if possible
Other things include delocalized (resonance) coordinate bond and it will be specified on how many atoms electron cloud being donated is delocalized , colour [photon accepted and released's wavelength can be correlated withe energy gap between HOMO and LUMO and the electron gets excited to the next lowest energy orbital i.e. LUMO, and then dexcites , photon's energy =hv and can be used to measure crystal field splitting energy with is the energy gap we are discussing], magnetic moment = (n(n+2))^1/2 Bohr Magneton {it's a unit} where n is the number of unpaired electrons in the configuration etc, Also, that energy gap increases rapidly with oxidation number and size and charge density {size becomes smaller as we move down in d block due to lanthanoid/actinoid contraction} so, pretty much any ligand is strong for 4d and 5d metals and for 3d, anything after and including nh3 is strong and anything before and incuding H2O is weak except for Co+3, by strong and weak i mean gap is or is not big enough to cause pairing,
Extra :
If there is one unpaired electron and all ligands are strong, then transference will take place if inner orbital complex would be formed {meaning, the electron jumps to a higher level for the good of them team, and the emptied orbital can take part in bonding}
If there are 2 unpaired electrons and again, all ligands are strong, again they will be forcefully paired if dsp2 i.e. CN=4 is there. {meaning would be formed if they got paired}
Any metal with oxidation number > 4 , All ligands are strong for it like Ni+4.
and other factors like number of d electrons, proton number etc also influence it but basically, it increases with positive charge on central metal
from here ligand theory starts