If you want to phone a taxi in Granada you either have to know the number of a taxi driver or you have to phone a taxi company.

If you get a good honest taxi driver it is worth asking for their card so that you can use them again.
I have about 3 taxi drivers who I use all the time.

In the city of Granada taxis are white and have a green stripe down the side.
If they have a green light on you can hail them.
If they have the OCUPADO sign up with a red light they are taking someone.

There are two main taxi location numbers.

958 28 06 50
958 13 23 23

You can't book a taxi.
When they ask you for your current location they will locate the nearest taxi and send them.
Thay are very bad at dealing with people who don't speak Spanish.

The system is semi-automated and seems to be for their benefit rather than the customer.
If they manage to find a taxi for you an automated voice tells you the number of the taxi.
If they fail they don't tell you that they failed and this leads many people to believe that a taxi is coming when it isn't.

So my advice is to try to get to know a good taxi driver and phone him/her directly.
If that fails then you will have to phone one of the number above.

If you are staying with someone who is helpful they will be able to phone a taxi driver for you.
I know that granadainfo will arrange taxis for people.