There's no train connection with Addis Ababa Airport.
Car and bus
The airport is situated in Bole, 8 kilometers southeast of Addis Ababa's center, in the outskirts of the city. The airport is easily accessible by rental car. From the center of the Ehtiopian capital you take the Africa Avenue southeast and continue via Bole Road to the airport. From other districts you can follow the Ring Road. The way and exit to the airport are clearly signposted.
There's no regular bus service to Addis Ababa. Minibuses do run to the capital, but they don't stop in front of the terminal. If you walk across the parking lot to the main road, you can stop a blue minibus there. A ride to the city center takes about 30 minutes and costs 15 birr (the Ethiopian currency).
Car rental Addis Ababa Airport
You can find counters of car rental companies in the Arrivals Hall. Several rental companies are present at Addis Ababa's airport, including Alamo, Avis, Europcar, Hertz and Sixt. You can also rent a car from local providers via National Tour Operations or travel agencies.
There are many taxis outside the Arrivals Hall. Some use a meter, but most of the time you need to negotiate about the price. Make sure to agree on a price before getting in. A taxi ride to Addis Ababa's center costs about 60 birr.
Outside the terminal there's a parking lot for short and long-term parking.