Do an online search where you will find several options, one being the Florida Veterinarian Medical Association's official website. This site and sites like localvet.com have a full listing of every registered veterinarian in the state of Florida. The sites are simple to navigate and can help you with even minimal details.
Select the city, county or if you know one, you can put in a particular veterinarian's name. On the Florida Veterinarian Medical Association's site, one of these three pieces of information is all you need to conduct your search.
Select the veterinarian option that best suits your specific situation. The listings will have the veterinarian's name, business address, and more often, a phone number. Some of them will also include the business hours for the clinic and the particular veterinarian's specialties.
Check the Yellow Pages if you don't have a computer handy. You might first check the A's for keywords like Animal care. You should obviously also check the V's for Veterinarians. These listings, if there is any, should at the very least be able to provide you with a phone number to call.
Look through the local phone book if the Yellow Pages are no help. You should again look for keywords like Animal care or Veterinarian.
Ask someone, if neither the Yellow Pages nor the phone book are any help. Try stopping in a local gas station and asking the clerk. If you're looking for a more of a reputable source, then try stopping at the local chamber of commerce. No one knows Florida better than people who live in Florida. If there is an animal clinic that is unlisted, the locals should be able to help you find it.