Balance the iodine atoms:
2 I- --> I2
The Mn in the permanganate reaction is already balanced, so let's balance the oxygen:
MnO4- --> Mn2+ + 4 H2O
Add H+ to balance the 4 waters molecules:
MnO4- + 8 H+ --> Mn2+ + 4 H2O
The two half-reactions are now balanced for atoms:
MnO4- + 8 H+ --> Mn2+ + 4 H2O

