There is a train (Cercanias)outside the Malaga airport that will take you to the city center. In the other direction, the train goes along the coast to Fuengirola, with stops at Torremolinas, Benalmadena etc. The trains run about every half hour.
There is a stop for the main train station (RENFE) which is near the Malaga bus terminal.
See my response in the "Getting From Malaga To Nerja" Topic for the bus schedules.
Train Map