I live and work in Georgia but the company I work for and get paid by is in Florida how do I file for state tax

You file with the state of GA as a resident. Your employer should be withholding GA state income tax from your paycheck. Otherwise you will have a big tax bill due, and starting with the 2nd year you may be facing interest charges for underpayment of GA taxes during the year. Alternatively you can file quarterly estimated tax payments with GA to avoid the possible interest charges.

Yes, your company should be doing the Ga withholding. And you just file. Where their main office is, has no bearing on it.
I work in GA and my main office is in MO