Nerja is just forty five minutes drive from Malaga (Pablo Picasso)  international airport and there are a couple of ways to get here from the airport if you haven’t arranged a hire car.
The cheapest and by far is by public transport. A shuttle bus runs from just outside the arrivals hall to the main bus station in Malaga every thirty minutes from 0700 and the last one varies between 2300 and 2400 but this would make you miss the connection to Nerja at Malaga bus station. The journey takes between an hour and an hour & fifteen minutes.
Make sure you allow time for any queues at the bus station. The cost is around a euro.
You can also take the train from the airport into Malaga (where the bus station is right next door to the train station) but it means dragging your luggage to the train platform which is quite some distance from arrivals. Follow the signs for trains.

At the bus station you need to find the Alsina Graels (being rebranded and renamed Alsa ) ticket office to buy your tickets. Tickets to Nerja are 3.85 single or 6.93 return (Nov 09 prices)
The first bus leaves the station at 0700 and the last one at 2300
You can check timetables and prices at the www.alsa.es which is in english as well as other languages and also for other destinations or click here

From there the bus takes between an hour and an hour and fifteen minutes and you arrive in Nerja at the top of the town at the bus staion.

You could just jump in a taxi at the airport but the transfer is 90 euros. If you pre-book a taxi from one of the taxi firms in Nerja this will drop to 69 euros and the driver will meet you in the airport.
You can pre-book your taxi online at www.nerjataxis.net or click here
There is no train to Nerja from Malaga.

Directions if you are driving from the airport:
Leaving the airport follow the signs for Malaga and you will pick up the A7 (E15) motorway.
Follow the sign for Motril & Antequera (again A7/ (E15) but the first sign for this route is actually over a lane that takes you to an industrial estate, make sure that you are careful to miss that turn off.

From then on you are straight all the way with no turn offs. About 45 mins drive.

Parking can be a bit of a nightmare here in the height of summer, but the  opening of another underground car park in Verano Azul to the west of Nerja near Supersol has helped.
The other large underground car park is to the rear of The townhall and is well signposted.