Taxis in Spain are generally less expensive than they are in other European countries, but you still need to watch out and make sure you are not being ripped off. If you try to hail a cab from an airport or train station, they will generally have to charge you standard rates that are pre-determined.

However, if you get a cab from a random location late at night and don't speak the language too well, the drivers can try to pull one over on you. If you get in a taxi and the meter is not running, you should ask the driver why not. Sometimes you can actually save money this way by agreeing to a fare before you get going, but unless you speak the language this can be difficult and drivers can sometimes misunderstand or get insulted if you say the wrong thing. In Granada, this is the same as it would be in Barcelona or Madrid.

Another thing that can either increase or decrease the cost of a taxi ride would be the amount of luggage you have. Sometimes if you have a lot of luggage on you the driver will charge more. The reasoning behind this is that they assume you are tourists and can charge you more, and they are charging you for helping with the luggage. Drivers sometimes ask for more money because it is a weekend or a public holiday.

http://www.granadainfo.com/taxiinfo.htm gives an indication of the fares and charges. 

Rental cars follow the same procedures as in any other country. You must have proper ID and insurance. You can either pay up front or after you return the car, but it depends on what agency you use and some other variables. Roads in Spain are very good, so this is a good option, especially if you want to take your time driving throughout the country. Car rentals are best found at the airport or train station. Be aware that a lot of the ones within the city do not work on Sundays and public holidays or have restricted hours of work.