How do I know when I can turn right on the traffic light (when it is red) in Fort Lauderdale and Orlando?

In Florida, you can legally turn right on a red light (unless you're looking at a red arrow) after you come to a complete stop, and make sure there's no on-coming traffic.

Any time there is no sign that says no turn on red, OR a RED ARROW light. Otherwise, after a full stop, you can turn right on red anywhere in FL when the coast is clear.

You can turn right on a red signal if the way is clear, unless:

The road to the right is no-entry from the direction you're entering from

or

A "NO TURN ON RED" sign is displayed at thr intersection.

You can turn right on red in most states (Florida included, I believe) after coming to a full stop and when traffic permits turning into the near lane, providing you yield to pedestrians and no signs or signals prohibit such a turn.

If it doesn't say you can't, then you can.