There's no direct train connection with Kota Kinabalu Airport. The nearest train station, of Sabah State Railway, is located two kilometers north of Terminal 1.
Car and bus
The airport is situated 8 kilometers southwest of Kota Kinabalu's city center. From the center you can reach the airport by rental car via the Jalan Lintas Road (A1) which connects with Jalan Kepayan, the road that runs along the terminal. The way to the airport is clearly signposted.
Regular buses 17 and 19 don't stop at the terminal, but on the road past the parking lot (Jalan Kepayan). These buses only run once an hour. It's easier to take a minibus to the city center.
Car rental Kota Kinabalu Airport
You can find counters of car rental companies in the Arrivals Hall of Terminal 1. Four rental companies are present at Kota Kinabalu Airport, one international company (Hertz) and three local car rental providers: Borneo Trails, KK Leisure Tour and KMT. There are also counters of car rental companies in Terminal 2, but only of local providers.
Taxis are the only means of public transport between Kota Kinabalu Airport and the city center. You can buy a ticket for the taxi in a kiosk outside the Arrivals Hall (standard rate 30 ringgit). You can also choose to ignore the ticket kiosk and walk to the road in front of the terminal. It's cheaper to stop a taxi here. Make sure to agree upfront on a price though.
There's a short and long-term parking lot outside the terminal.