Take the train from Malaga Airport to Fuengirola train station. The Malaga Airport train station is straight in front of the exit door from the Arrivals area.
The trains leaves every 20 minutes. You can buy tickets from the automatic ticket vending machine or the ticket office in front of the platform access barriers downstairs.
When you get to the underground Fuengirola train station, come upstairs and walk one block towards the sea, the bus station is right there on the corner. The bus you want to catch is the bus to Marbella, further down the coast. Club La Costa is just outside Fuengirola in the Mijas Costa area. Check here for a listing of bus stops between Fuengirola and Marbella. There is a big bus stop on the main road.
You could even take a taxi to La Cala from the taxi rank right outside the train station - you will have saved a lot of money by taking the train so far. Watch your pockets, bags and belongings on the train and getting on and off the train when you are always off balance. I always give this advice to travellers anywhere.
Check here on the Costa del Sol bus page for the Fuengirola Bus Schedules showing buses leaving from Fuengirola.
Here is a Gomarbella blog also about how to get to Club La Costa Mijas and the bus stop you get off at. With all this information I'm sure you'll get there easily! Have a great visit to Club La Costa!