There's no train connection with Amman Airport yet, but it's planned to construct a rail connection between the airport and the Jordanian capital's center. It's not clear when these plans will materialize.
Car and bus
The airport is situated 32 kilometers south of Amman and is easily accessible by rental car. From Amman's center you take the freeway with road number 15 south. The exit to the airport is right before the town Al Jizah and is clearly signposted.
Every 30 minutes (at night between 22.00-07.00 every hour) an Airport Express Bus (Tel. +962(0)6 592 7665) leaves from the airport to Amman's center (Abdali). The ride takes about 45 minutes and a bus ticket costs 1.50 dinar.
Car rental Amman Airport
You can find counters for car rental in the Arrivals Hall. There are various rental companies present at Amman Airport including many local suppliers and two international ones: Budget and Europcar. You can also book a rental car in advance using the services provided by EasyTerra; they compare the rates of several providers in a single quote.
Taxis at Amman Airport are available 24 hours a day. You buy a ticket at a kiosk. There are set rates which are clearly indicated on a sign. For reservations and information you call +962(0)6 4451 302. Official taxis are yellow with a green logo on the side.
In total there are six parking facilities with a total capacity for 1400 cars. Parking fees are extremely low. For a full day parking you pay less than 4 dinar.