Panama City has no shortage of taxis, operating according to a fixed-price system. Never ask the cost of a trip – this tells the taxi driver that you don't know the price. The minimum is $1.50 and nearly all trips will cost this, or slightly more. Getting from one end of the city to the other will be about $3. The Miraflores locks cost $5. Getting to the international airport is $15 - $20, getting into town from the airport is $20 - $30.
There's also a network of buses, but these run on a confusing and convoluted schedule. A bus to the international airport leaves from Plaza Cinco de Mayo and takes 45 minutes to an hour. Be sure to take the Tocumen Corredor bus, the other Tocumen can take up to two hours. A bus to the canal leaves from the same place. Look for buses marked Gambo or Paraiso.