Details of flight plans may as yet change with the airlines’ summer schedules.
Below you will find some basic travel information:

Within Europe, some low-cost carriers offer direct flights to Granada, so checking the web sites of carriers such as RyanAir, EasyJet, Veuling, and low-cost travel web sites will be worthwhile. (would be nice to link to some of these when you have time)

Depending on where you fly from, you may need to connect through Madrid or Barcelona for a flight to Granada. Alternatively, you might fly to Malaga and transfer by ground to Granada. This may be especially convenient if flying from the UK.
Malaga airport is 125km from Granada. It takes 1hour 30 minutes from Malaga to Granada by car. The best way to get to Granada by public transport is to catch a bus from the estación de autobuses in the centre of Malaga. There are frequent buses which connect the airport with the bus station. There are buses every hour until 22.00 and the bus journey takes 2 hours. It is difficult to get to Granada by bus if you arrive after 10pm. A taxi from Malaga to Granada costs approx 120 Euros.

The airport is located about 8 km outside the city of Granada. There are several bus services from the airport. Some of them are operated by the airlines and the prices are around 6 Euros per person. All of them at some point go down Gran Via de Colón then Reyes Catolicos in the centre of Granada.

The best way to get to the airport from the centre if you don't want to walk through the streets with your luggage is by taxi which costs approx 26 Euros. There is supposedly a fixed taxi fare for taxis from the airport to the city centre (25 Euros for the centre of Granada, and 30 Euros for the Albaicín) so it's a good idea to ask how much it will cost before getting in the taxi. The taxi driver should not use the taximeter. There is also an airport bus with a frequent service which drops you in the centre of Granada. The cost is 3 Euros.

There are also daily flights to Granada from Barcelona and Madrid but they are not cheap. (Tip: When there is a flight from outside Spain with a connecting flight from Madrid/Barcelona to Granada they may have problems with the coordination of the luggage so organize yourself accordingly- it will be still very warm in October.)