If you are from the UK, as you already know, Americans drive on the 'wrong' side of the road. The times when you are more likely to make a mistake with this are when you are tired, when you first set off in the morning and when you are turning or pulling out of a driveway or garage/gas station. Take special care to concentrate at these times.
All the rental cars are automatic so you don't have to worry about changing gear but sometimes their handbrake is different to UK ones, i.e. a foot pedal up under the dashboard. Make sure you understand the controls of your rental car before you drive away from the rental station and, if in any doubt, ask!
If you are the driver, make sure you carry your driving licence and car rental documents with you at all times.
Some rental cars lock the doors for you automatically when you reach a certain speed so don't wonder what is happening! If your car doesn't do this for you, it is wise to lock them yourself manually.
Keep your windows closed as this helps your air conditioning to work properly so that you stay cool and it also keeps bugs out of the car.
If you are parking, try to find a lit area or park under a light, if you can.
Don't leave valuables, jackets, etc in the car interior or maps. Make sure that you put these in the boot (trunk) of your car. Don't leave your camera in your car as the heat inside when you return may have ruined your film. Never leave kids alone in the car.
Like at home, there are speed restrictions which are sometimes enforced by radar. Make sure you are under the speed limit or you risk an on-the-spot fine. Note that some roads also have minimum speed restrictions.
Yellow school buses have special rules in USA. If a school bus stops, all traffic must stop in both directions until the school bus moves off. If you are driving in the opposite direction to a school bus on a dual or more carriageway, you don't have to stop.
If it rains, it is compulsory in Florida to turn on your headlights
at the same time was your windscreen wipers. If there is a storm and you
have difficulty seeing the road ahead, pull over and stop until
visibility improves.
If you are pulled over by an officer, stay in your car and let the
officer approach you.
If you are unfortunate enough to have an accident or are bumped from behind in a deserted or dark area and there is likely to be minimal damage, indicate to the other driver to follow you. Drive to a populated area (a garage/gas station is ideal) before you get out of the car.
Make sure that you follow the instructions on your rental agreement and inform your car rental company if you have an accident.
The drink driving laws in Florida are extremely strict and driving after drinking will invalidate your rental car insurance too. You are not allowed to have alcohol in your car so, if you have this, make sure that this is stored in the boot/trunk. Please don't endanger your life or that of others - if you are going to drink, please don't drive!