Identify the oxidation states of manganese and iron in the reactants and products to determine which species are oxidized and which are reduced. Mn in MnO4^- is typically +7, Fe^2+ is +2, and in the products, Fe^3+ is +3, MnO2 contains Mn in +4, and Mn^2+ is +2.
Write the half-reactions for oxidation and reduction separately. For example, the oxidation half-reaction involves Fe^2+ being oxidized to Fe^3+, and the reduction half-reaction involves MnO4^- being reduced to either MnO2 or Mn^2+, depending on the product given.
Balance each half-reaction for atoms other than H and O first, then balance oxygen atoms by adding H2O, and balance hydrogen atoms by adding H^+ ions since the solution is acidic.
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 and simplify to get the balanced overall equation.