Identify the oxidation states of elements in the reactants and products to determine which species are oxidized and which are reduced. For example, in H2O2, oxygen is in the -1 oxidation state, and in ClO2 and ClO2⁻, chlorine has different oxidation states.
Write the half-reactions for the oxidation and reduction processes separately. For instance, write the oxidation half-reaction for H2O2 converting to O2, and the reduction half-reaction for ClO2 converting to ClO2⁻.
Balance each half-reaction for all atoms except hydrogen and oxygen first, then balance oxygen atoms by adding H2O, and hydrogen atoms by adding H⁺ ions (since the reaction is in aqueous acidic solution).
Balance the charges in each half-reaction by adding electrons (e⁻) to the appropriate side so that the total charge is the same on both sides of the half-reaction.
Combine the two half-reactions by multiplying them by appropriate coefficients so that the electrons cancel out, then add the half-reactions together. Finally, verify that the number of atoms of each element and the charges are balanced in the overall equation.