Everything from the 2 lessons of this topic on a few pages: the key idea of each lesson, the diagram to remember, the points to learn and the traps examiners set. Read it, cover it, test yourself.
An oxidation number is the charge an atom would have if all its bonds were ionic. Elements are 0; a simple ion has its charge; the numbers in a compound add up to 0, and in an ion to the ion's charge. Oxygen is usually −2, hydrogen +1 and fluorine always −1. Oxidation is loss of electrons, an increase in oxidation number; reduction is gain of electrons, a decrease. An oxidising agent is itself reduced; a reducing agent is itself oxidised.
The oxidising agent is the species that is reduced, because it takes electrons from something else. Students often name the species that was oxidised instead. Also remember that oxidation numbers are written with the sign first (+3), while ionic charges are written with the sign last (3+).
A half-equation shows one species gaining or losing electrons. In acidic solution balance it in four steps: the element changing oxidation number, then O with H2O, then H with H+, then charge with electrons. The number of electrons equals the change in oxidation number. To combine two half-equations, multiply them so the electrons lost equal the electrons gained, add them, and cancel anything that appears on both sides. No electrons may remain in the final equation.
Electrons go on the left in a reduction and on the right in an oxidation, and they must all cancel in the full equation. A final equation that still shows e− has not been combined properly. Always finish by checking that the charges balance as well as the atoms.