The main international air ports in Costa del Sol is located near Malaga. The airport operator is Aena. Information is available from their web site.  Haven't  got the ticket yet. Click here for discount flights.
 

Transfer may already be arranged by your tour operator, else Taxi is not to expensive. Max persons in one Taxi is 4. Have your destination written on a piece of paper, and ask for the price.  If you are more than 50 Km. away from your final destination, then consider to rent a car.
An alternative is to book transfer together with your hotel. This service is offered by www.alpharooms.com . An other possibility is www.resorthoppa.com  or A2Btransfers.com

If you are planning to use public transport, the trick is to ask the tourist office at your destination. To find their address &Tel. or e/mail, use the official tourist web site for Spain: http://www.spain.info   Look in section for destinations, or use their search.
You can also look in section for "usefull web sites"   here, if a local web site is listed.
 

There is a costal train, from Malaga to Fuengirola, stopping at the airport. If you are arriving in the airport, take the lift to the departure section. Some 10 minutes walk from there. Ticket must be purchased from ticket machine before boarding the train. Euro coins needed. Train is half hour from approximately 7.00 hours to 22.00 hours.
 

Are you going further along the coast that Fuengirola, then there is a bus from the airport to Marbella. Approximately every 2 hours from 6.00 hours to 23.00 hours.