This is a very common question.
In my opinion it is best to buy a ticket to Granada from Malaga in advance.
It makes things easier if you aready have the ticket and it is one less thing to worry about on arrival.
To buy tickets online go to
https://alsa.es If you miss a bus they normally let you onto the next bus without paying again as long as you have a ticket.
Shuttle bus from Malaga Airport to Malaga City CentreIt is easy to get to Malaga bus station. There is a shuttle bus from Malaga Airport to Malaga City Centre, there are 10 bus stops along the way. The total journey time is around 15 – 25 minutes. It costs just about 3€ and you can pay the driver direct. The bus station stop is Estación de Autobuses (Maria Zambrano). There is a bus around every 20 – 25 minutes from 7am until midnight from the airport.
Alsa Bus has a bus every hour from Malaga Bus Station to Granada untiI 20:00h.
There are many more buses from Malaga Bus station than from the airport.