1. Write the oxidation and reduction half-reactions by observing the changes in oxidation numbers and write these separately.
                                           
Oxidation half-reaction:          

Reduction half-reaction:     

2. Balancing the oxidation half reaction.
(i) The balance I atoms are done by multiplying HIO₃ by 2.
                              0             +5
                              
(ii) Add 10 electrons towards R.H.S. in order to balance the changes on iodine atoms. 
                                         
(iii) Balance the O atoms by adding six H₂O molecules towards L.H.S.
                           
(iv) Balance H atoms by adding ten H⁺ towards 
R.H.S.
                  

3. Balancing the reduction half reaction. 
 (i) Balancing of N is not required as the number of each N is one on both the sides. 
                  +5                   +4
                HNO₃            NO₂
(ii) Add one electron towards L.H.S. in order to balance the charges on the nitrogen atom. 
                 +5                     +4
                  HNO₃ + e^-     NO₂
(iii) Balance O atoms by adding one H₂O molecule towards R.H.S.
                 5                   4
               HNO₃  + e^-       NO₂ + H₂O

(iv)  Balance H atoms by adding one H+ towards
L.H.S.
         +5                           +4
        HNO₃ + H⁺ + e^-        NO₂ + H₂O
                                     (Balance reduction half reaction)
4. Multiply balanced reduction half-reaction by 10 to equate electrons and add both the half reactions. 
              
This is a balanced redox reaction.