Our company is located in GA, but several of employees are FL residents. How do I go about handling their tax withholdings?

The important question is: where do the FL residents work? If they commute into GA to go to work then you should be withholding GA income taxes from their wages, just as for GA residents. But if they work in FL then you should not be withholding GA taxes, as these employees neither live nor work in GA. And since FL does not have an income tax you do not need to do anything regarding FL taxes for these employees.

They work here in GA and commute to GA from FL. Also, what do they need to do about taxes paid to GA when the file in FL?

They work here in GA and commute to GA from FL. Also, what do they need to do about taxes paid to GA when the file in FL?

Since they work in GA they must pay GA income tax. They file tax returns in GA as non-residents, and paty taxes on the wages they earn in GA (they do not pay income tax to GA on other non-GA based income they may have, such as interest, dividends, capital gains, the spouse's job if he/she does not work in GA, etc). They do not file an incomre tax return for FL, because FL does not have an income tax. However, if they commuted into GA from a state that has an income tax (like say SC), they would be filing a non-resident return with FL and a resident return with SC. But from the employer's perspective, as a GA employer all you need worry about is withholding GA tax for your employees who work in GA.