Trip from the airport to the centre of Chengdu:
It's best to take a taxi. Bargaining, you should be able to negotiate a 50-60CNY fare (20-30 min.). Ask your hotel to arrange the trip for you at this amount, or do so yourself with the driver.
In any event, there is also a Shuttle Bus (no. 303) that delivers you in the city centre in an hour (last stop). Tickets are purchased in the ticket office just outside the airport (10CNY). This bus will drop you on Renmin South Road 2nd Section, very close to the river. Depending on where you hotel is, either walk or take a taxi, which shouldn't run you more than 12CNY.