I lived in Georgia for some of 2008 then moved to Florida. I worked in Florida for the whole year. How do I file state tax and how do I go about it?

You were part year resident of Georgia. You must report the income you earned during that period on the Georgia tax return.
If you are still resident of Georgia, that is your moving from Georgia is temporary, then you must report income for whole year to Georgia.
Read Your U.S. Tax Return: Working or Living in Two or More states