Getting into Granada
Granada (map) has a national highway called A44 just around the city. There are many exits on this highway. When you are on the A44, wait for exits with direction city center. The driver can easily get off and on the A44, in either direction.
Going to Sevilla
Go where the A44 crosses the A329 (location on map), and get on the A329 towards the A92. This is the highway between Sevilla and Granada.
Going South or North
Going to Valencia/ Barcelona
Get any of the entrances next to the A44 and use the direction of Lorca/ Guadix (A92 and later A91). Best thing would be to wait for someone who actually is going into that direction since the A44 crosses the A92 after 5-10 minutes.