Write a balanced equation for the following reduction-oxidation reaction.

SO3–2 + MnO4–SO42– + Mn2+
__SO32–(aq) + ___MnO4–(aq) + ___H+(aq)--> ___SO42–(aq) + ___Mn2+(aq) + ___H2O(l)

I have no idea how to do this type of problem, care to explain?

Try this site. It would take 30 minutes for me to type the directions. Hint for first one.

S goes from oxidation state of +4 on the left to +6 on the right. Mn goes from +7 on the left to +2 on the right.
http://www.chemteam.info/Redox/Redox.html
This site covers it all.