Casco Viejo, like the rest of Panama City Panama, has a yellow flood of steady and endless taxis. Wave them over from a busy curbside, such as outside of a hotel or commonly visited area of town. When they ask you where you want to go, it will help if you have a landmark near your destination in mind. Well-known locations like Albrook Mall, Mercado del Marisco, or Multicentro, are good places to start and easy to make your way to and from. Asking to be taken to a very specific area in a lesser known section of town is nearly out of the question.
It's very important to ask “Cuánto?” before getting into a taxi. You always want to ask how much because fares are negotiated before travel. If you just get in, then they know you're an outsider and you'll be charged the gringo rate. Getting from Casco Viejo to Multiplaza, for example, will cost 3 or 4 dollars, still much cheaper than taxis in major US cities.
Do not let your feelings be hurt if the taxi drives away once you tell them where you want to go, because they typically only pick up fares with a destination preferable to them. Also, do not be surprised if your driver picks up other passengers while en route. If you're a solo traveler going a long way, then your taxi driver will try to fill the car with others headed, roughly, in the same direction.
Most taxi drivers in Panama City, Panama tend to have a good disposition. They'll usually ask if you want the windows down or the AC on. If you're from out of town, they might ask you what sights you've seen. They are especially friendly if you're being charged the gringo rate!
And lastly, in general, they drive pretty crazy in Panama City. Horns honk constantly and hand gestures wave impatiently; its just part of the experience. If you're walking, then make sure you look both ways before crossing the street. And if you succeeded in catching a taxi, it's recommended just to buckle up, sit back, relax, let the drive do their thing and enjoy the views of the city until you reach your destination.