Rental car:   Cars can be rented from many locations including at the airport, hotel, rent-a-car offices or tour operators. Prices vary and so does the quality of the car and insurance coverage as all the major car rental companies are available also smaller local companies.  

Highways:   Gran Canaria was the first of the Canary Islands to develop its highway system, and it is a system which remains up-to-date to this day.   There are three superhighways which help alleviate road traffic around the island and which are particularly useful for travel to and from the airport.  
 

Taxis:  Cabs are available everywhere and are not expensive for short in resort trips however they are generally pricey for round the island trips.

Ferry:  There are ferry boats and water buses available for use by travelers.  Many people use these to get from Gran Canaria to the other Canary Islands, because they are considered an inexpensive method of travel.

Bus:  The reliable local bus system is inexpensive and can be used easily by anyone and buses run on time and frequently between the main centers and round the island. Information about  buses can be had from most hotel receptions. More is online at http://www.globalsu.net/index_en.php