There is a frequent bus service between Almuñecar and Granada.
There are about 9 buses each way per day
The price is about 8 euros.
The bus to Granada takes you to the Granada bus station.
To get to the centre of Granada get on a 3 or 33 bus which will take you to the Cathedral.
You can book tickets using this site.http://www.alsa.esCAR
It takes about 50 minutes from Granada to Almuñecar by car using the autopista (motorway).
Here is a list of car parkshttp://granadamap.com/car_parks.php
If you are going to the Alhambra go to the Alhambra car park (use link above)
For stays of more than 24 hours in Granada it is best to go to Severo Ochoa Car parkhttp://granadamap.com/so/index_en.htm
If you have more time and you don't like motorways there is an incredibly picturesque road from Almuñecar to Granada.
Follow the signs from the centre of Almuñecar to Otivar or Jete.
If you go this way it will take about 90 minutes.
There are lots of tight bends, the views are spectacular.