There's no train connection with Lagos Airport.
Car and bus
Lagos Airport is situated 22 kilometers northwest of the city center. The airport is easily accessible by rental car. There's a freeway from Lagos Airport to the city. Depending on the traffic, you can cover the distance in 30 to 60 minutes.
Car rental Lagos Airport
You can find counters of car rental companies in the Arrivals Hall. You can rent a car from one of the two international rental companies present, Avis and Hertz. Keep in mind though that, apart from some freeways, the roads in Nigeria are in bad condition.
Regular buses and minibuses run between the airport and the city center, but they are often crowded and moreover not very safe.
Taxis are by far the easiest and safest way to travel from the airport to Lagos. They can be found outside the Departure Hall, so upon arrival you first need to go upstairs. Make sure to agree on a price upfront. You need to seriously negotiate to get a 'correct' price.
A parking garage has been built near the new terminal MMA2. You pay 100 naira per hour. The day rate amounts to 1,500 naira. The garage is connected with the terminal via a corridor.