Hiring a car in Chengdu is not advised due to heavy and chaotic traffic, especially at rush hour times. Metered taxis are available, though difficult to find in some areas. Note that it is necessary to have your destination written in Chinese as most drivers don't speak English.
There are plenty of public transport options, most of which are marked on tourist maps available from the airport, railway station, and souvenir shops.
Public transport in Chengdu is mostly comprised of an extensive bus network. There is a free shuttle service that links all parts of the city centre. The other half of Chengdu's public transport is the metro, which connects the North and South Railway Stations. A second line, running northwest and southeast, has recently been completed. Trains are regular and safe, if a little crowded during rush hour. Be sure to check the operational hours as the metro does not run late into the night.