I am working for a company based in Alabama. We are at a jobsite in Georgia and I live in Florida. When they take taxes out of my check for working in Georgia do I get them back at the end of the year when I file a tax return? My legal residence is in Florida.

If you work in GA you pay income tax to GA on those wages. It doesn't matter that the company is based in AL.

At the end of the year you will have to file a non-resident GA tax return. And no - you won't get those taxes back.