Avanaza has services direct from the airport along to Marbella, Estepona and Algeciras. All start and finish at Terminal 3 – Llegadas (Arrivals)
More details on the Avanza website
Málaga Shuttle Bus is another option at just 18 euros to/from the airport. Be aware that flights TO the airport have to be booked 36 hours in advance. Ryanair flights FROM the airport do NOT need to be booked in advance, although it would seem sensible! Other flights do not have guaranteed connections and you must book in advance. Full details here.
Taxis are available and you should expect to pay 65 euros from Marbella and a bit more from Puerto Banús or Nueva Andalucia. The rates are slightly higher in Semana Santa, August and at night/weekend.
If you are on a budget, you could take a local bus to Fuengirola bus station for less than 3 euros and then a RENFE train direct to the airport. That would give you a total price of less than 6 euros! Although it may be the least expensive option you should leave yourself nearly two hours for the journey.