Well, you could fly. It takes an hour, and goes direct from the airport!
By train, you would have to get the metro to Madrid centre, then the
train would take about four and a half hours.
The bus takes 6 hours, from the airport to Granada.
http://www.alsa.es/portal/site/Alsa
It appears that you can't buy tickets for the bus online.
--
Pete Clark
Local sites for Local People in Spain
http://localFaces.net
Yes, you can book online. You can't book online for today. I hadn't
changed the "departure date"!
The bus would be much more interesting, if you can manage 6 hours in a
bus after what could be a long flight. And if the traveller can make
the bus departure time, as there only seems to be one bus per day, at
10:30