There's no train connection with Doha Airport.
Car and bus
Doha Airport is situated about 4 kilometers southeast of the city center. The airport is easily accessible by rental car via Al Matar Street or Ras Abu Abboud Street. The way to the airport is clearly signposted along both roads.
There are no bus connections between the airport and Doha, except for shuttle busses to large hotels.
Car rental Doha Airport
You can find a counter of car rental companies in the Arrivals Hall. Eight rental companies are present at Doha Airport: Avis, Budget, Europcar, Hertz, Mustafawi, Prestige, Sixt and Thrifty. You can also book a rental car in advance by using the service provided by EasyTerra; they compare the rates of several providers in a single quote.
Taxis are the only means of public transport between the airport and Doha. The orange-white taxis can be found outside the Arrivals Hall. A ride to the city center costs about 25 riyal.
There are large, covered parking lots near all terminals. You can park your car for 2 riyal per hour. The day rate for parking at Doha Airport amounts to 45 riyal.