Identify the oxidation and reduction half-reactions in the given redox reaction. Manganese in MnO_4^- is reduced from +7 to +2 in Mn^{2+}, and iron Fe^{2+} is oxidized to Fe^{3+}.
Write the half-reactions separately: the reduction half-reaction for MnO_4^- to Mn^{2+} and the oxidation half-reaction for Fe^{2+} to Fe^{3+}.
Balance each half-reaction for atoms other than H and O first, then balance oxygen atoms by adding H_2O, and balance hydrogen atoms by adding H^+ ions (since the reaction is in acidic conditions).
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 each half-reaction.
Multiply the half-reactions by appropriate coefficients so that the number of electrons lost in oxidation equals the number gained in reduction, then add the half-reactions together, canceling electrons and any species that appear on both sides to get the balanced overall equation.