If you have a tight budget, flying to Madrid and then traveling to Granada by coach, train or sharing a car may be a good option (check also Tips for those traveling from Málaga).
There are four terminals named T1, T2, T3 and T4. A free ("gratis") bus running every 10 min. connects the four terminals.
Iberia and associated airlines fly to T4, low cost airlines and almost everybody else fly to T2 or T1.
T1, T2 and T3 are within walking distance (15min, with moving walkways). Getting from the T4 to the other terminals using the free bus, takes between 20 and 30 min.
T4 is divided into the main building and a satellite building connected by a shuttle train. In case you arrive/depart from the satellite, be aware that it will take you 30 extra minutes just to get there from the main building.
Taxis between the airport and Madrid city center cost 30€ (fixed rate). If you go or come from terminal T4 the taxi driver would let you choose if you want to use the toll road (+2€ approx,) reducing the trip by 10 minutes.
A suburban train (RENFE Cercanias) running every 30min, connects the T4 with the center of Madrid. 2.60€.
There are also Metro stations in both T2 and T4.
Finally, there are several city buses connecting the airport with Madrid.
Granada is 420 km away from Madrid. Motorway all the way, it is an easy road. The trip can be done comfortably in under 4 hours.
Speed is limited in Spain in motorways to 120km/h, radars fire at 130km/h.
ALSA provides a coach service running a couple of times every day from the T4 to Granada.
There is a more frequent service running from Madrid "Estación Sur" to Granada. You can reach that station by train (RENFE Cercanias line C1 departing from T4 to Mendez Alvaro Station every 30 min, trip time 31min), Metro (departing from T4 and T2, between 50-70min) or taxi (20min).
See also Buses' discount.
Trains to Granada depart from Atocha Station, located in Madrid city center.
The airport is connected by train (RENFE Cercanias line C1 departing from the T4 every 30 min, trip 26min), coach (Exprés Aeropuerto), Metro (departing from T4 and T2, 50-70 min) and taxi (30 min).
For more specific advice don't hesitate to get in touch with the organizers or the local Perl Monger groups via email or IRC (#yapceu, #barcelona.pm at irc.perl.org).
Want a free ride or a place to pass the night in Madrid?
See Madrid car sharing.