To balance redox reactions you have to look at each of the elements in the reaction and see which ones have changed their oxidation number. To do this, assign an oxidation number to each element and compare the oxidation number of the element on the reactant and product sides of the equation.
If the element has gained one or more electrons it is said to have been reduced. If the element has lost one or more electrons it is said to have been oxidized. The rule is that the "oxidizing agent is reduced and gains electrons" while the "reducing agent is oxidized and gains electrons.
Once you have identified the elements whose oxidation numbers have changed you can begin to balance the oveall reaction.
The other thing you will need to determine is if the reaction is taking place under acidic or basic conditions. This will allow you to properly completely balance any redox reaction. If the reaction is acidic, use H+ on the left and HOH on the right. If the reaction is basic, use OH (-1) on the left and HOH on the right to balance atoms.
The first step is to take each element separately and balance the "half-reaction" for that element. Depending on the bare bones, unbalanced half-reaction you may be able to just balance with electrons or you may have to first balance atoms before you add the electrons.
Lets take an example so you can see what is happening:
FeSO4 + KMnO4 --> Fe2(SO4)3 + HOH
The important part of this reaction involves the ions actually involved in the redox reaction. The other ions are considered "spectator ions". The net ionic reaction is:
Fe (2+) + MnO4 (-1) + H (+1) --> Fe (+3) + Mn (+2) + HOH
The iron has been oxidized and the permanganate reduced:
Fe (+2) --> Fe (+3)
MnO4 (-1) --> Mn (+2)
Now balance the iron reaction by adding one electron to the product side.
Fe (+2) --> Fe (+3) + 1 electron
The second half reaction requires balancing the atoms first, then the electrons. Because it is under acidic conditions, H+ can be added to the left side as the source of hydrogen ions.
MnO4 (-1) + H+ --> Mn(+2) + HOH
B alancing the atoms gives us:
MnO4(-1) + 8 H+ --> Mn(+2) + 4 HOH
Now balance the electrons in this half reaction:
MnO4 (-1) + 8 H+ + 5 electrons --> Mn(+2) + 4 HOH
This is important: Check both half reactions so each has the same number of electrons. If not, use coefficients on one or both half reactions so the total number of electrons is equal in each of the half reactions.
In this case 5 electrons were added to the reactant side for the permanganate so you need 5 electrons on the product side for the iron. Multiply through by 5, and you get:
5 Fe (+2) --> 5 Fe(+3) + 5 electrons
You are almost done!
The final step is to add the two half reactions giving you:
MnO4(-1) + 8 H+ + 5 Fe(+2) + 5 electrons --> Mn(+2) + 4 HOH + 5 Fe(+3) + 5 electrons.
The electrons cancel out and you have your balanced equation.