There are no trains in Kuwait.
Car and bus
The airport is situated 16 kilometers south of Kuwait City and is easily accessible. From the city center the Airport Road leads to the airport. The way to the Airport Road is signposted at different locations in the city.
Bus 501 connects the airport with Kuwait City. The ride takes about half an hour and costs only 0.25 dinar.
Car rental Kuwait Airport
You can find the counters of car rental companies in the Arrivals Hall. Several rental companies are present at Kuwait Airport, including Avis, Budget, Europcar, Hertz, National/Alamo, Thrifty and Sixt. You can also book a rental car in advance using the service provided by EasyTerra; they compare the rates of several providers in a single quote.
There are plenty of taxis (Tel. +956 2431 9829) outside the Arrivals Hall. A ride to Kuwait City's center costs about 6 dinar. Make sure to agree with the driver on the price though before you get in.
A large short-term parking lot with places for 2500 cars is connected with the airport's Commercial Center. A bit further out you'll find a long-term parking lot.