Cartagena is located about 1000 km north of Bogota, so most visitors chose to arrive by air. You can either take a direct flight from Miami or you can transfer through the Colombian capital of Bogota. The flight from Miami is about 2.5 hours, and it is an hour from Bogota. The Cartagena airport is called Rafael Nunez and is a fully international airport.
A more exotic method of transportation into Cartagena is charter boat. If you have been vacationing in Panama, you can hire a charter boat to Cartagena, as this city is a port for charter traffic between the two countries. These charters are usually extremely small (no more than family of four can comfortably be accommodated) sailboats with one crew member. The trip can take up to five days, depending on weather and stops along the way.