When a reactant molecule becomes stuck to the surface of a catalyst it is known as adsorption.The usual way this happens is that the catalyst has lone pairs. The reactant can then bond weakly to the catalyst using pi electrons. This can happen with a varying number of bonds. The catalyst holds the reactant still making it easier for the reactant to attack with sucessful geometry. An example of this is the Ziegler Natta reaction.

The Alkyl groups will attack the Titanium and the pi electrons will fill the available bond sites on the Titanium complex.
Variable oxidation state catalysis can be demonstrated by usind Iron as a catalyst in the reaction between Thiosulphate and Iodine.
a) S2O82- + 2I- goes to 2SO42- + I2
b) 2Fe3+ + 2I- goes to 2Fe2+ + I2
c) 2Fe2+ + S2O82- goes to 2Fe3+ + 2SO42-
So as you can see the Iron is reduced to Fe(II) and is then oxidised back to Fe(III). So although the Iron is altered during the reaction course it is regenerated the same as the staring material at the end of the reaction.
In reaction a) The charges repel each other. Iron has a positive charge and so is attracted to the Thiosulphate and Iodine in b) and c). This attraction anables the reaction to proceed faster therefore lowering the activation energy and speeding up the rate.
There are 3 basic principles that control how d-electrons fill shells.
The Aufbau Principle says that when filling d orbitals electrons are placed in the lowest energy orbital so that ground state can be achieved.
The Pauli Exclusion Principle states that no 2 electrons can have the same 4 principle quantum numbers. Any 2 electrons in the same orbital must have opposite spin in keeping with this rule. This is simply because no 2 things, including electrons can be in the same place at the same time.
The Hunds Rule of Maximum Multiplicity Principle states that when electrons fill orbitals they will be placed as far apart as possible to reduce repulsion. This is because all electrons are negatively charged and 2 of the same charges will repulse each other.