The most convenient way to get a taxi is to use the taxi service available at the airport. You can visit a special counter in the airport building, pay the fare (approximately 20 JOD), receive a receipt, and present it when boarding the taxi. This option will get you to your destination in about half an hour.
Alternatively, you can take bus 24/7, which will take twice as long but is considerably cheaper at 3 JOD.