Here is how you do these. You can start with the topic you don't know and use as many of the steps as you need.
http://www.chemteam.info/Redox/Redox.html
I STRONGLY ADVISE YOU TO START BY PLACING A 2 AS A COEFFICIENT FOR HIO3 so that you are talking about electron loss/gain for the SAME number of atoms.
I has an oxidation state of zero on the left and a total of 10 (for both I atoms) in HIO3.
N has a oxidation state of +5 in HNO3 and +4 in NO2.
I can help you through it; you go as far as you can, post what you've done, explain what you don't understand about the next step.
Balance this equation using oxidation method:I2+HNO3---->HIO3+NO2+H2O
3 answers
I2+10HNO3 -----> 2HIO3+10NO2+4H2O
Good