Contact the Florida Department of Agriculture and Consumer Services, Division of Licensing, Post Office Box 6687, Tallahassee, Florida 32314-6687.
Typical wait time is a 4-6 weeks. Cost is (used to be) $140 for 3 yrs, then they extend it to 5 years at the same price if you decide to renew and I think they then go to a 10 yr renewal program but am not sure.
Be aware that this out of state permit simply allows you to carry a concealed firearm, it does not allow you to purchase a firearm in Florida - for that you need a in-state license with required training (and I'm not so sure they are openly willing to accept another state's permit as proof of training) which is provided by gun stores, I think. HTH and good luck.