http://www.granadatur.com/en/travel-transport/moving-around-in-granada/Last year I went to Granada by bus (from Madrid) and found it comfortable - albeit long. Thank goodness for MP3 players.
As far as I know, Granada only has one bus station, located on the Avenida de Juan Pablo II, on the northern (slightly western) end of town. As you walk out of the station you'll see the main road in front of you. There, directly beside the bus station is the city bus stop. Stay at the one on the same side of the street as the bus station with traffic going towards your right - towards downtown.
There, you'll get bus #3 (1.20€ - they'll make change for small bills or 2€ coins if you don't have exact change). Get off near on the last stop on the Gran Vía de Colón, right near the T-corner with Calle Reyes Catolicos - which is the same stop right next to the Granada Cathedral.
Get off the bus, continue walking in the same direction as the bus to the corner. You've come to a "T" in the road and there you'll see the magnificent statue/fountain of Isabel & Ferdinand on the Plaza de Isabel la Católica in front of you.
Cross the street as you can with the fountain on your right. I BELIEVE now (because of road works on the normal route leaving from the Plaza Nueva) here is where you'll get the #30 bus (1.20€) going up to the Alhambra right on this small plaza. The bus will go uphill on Calle Pavaneras, going left-straight from the plaza-fountain (which is on your right).
As I said, this is a temporary route, modified because of the road works on the original route. Be sure to look at Google Maps as well as Google Street View to see what you'll be seeing - before you see it on the spot!
If you have any more questions, just ask!
Saludos,
GranadaMan
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