Keeping it nice and simple; if you're considering car-hire you can check prices at most of the companies in one go using the form above and find cheap, buget car rental from the UK or any European country:
One you have your cheap car hire of course you'll need your driving licence if you want to hire a car, along with your passport. if you don´t have a license with a photo on it. Most companies require the driver to be 21 years old or more with a clean license and at least one years driving experience. If the police stop you and you haven't got your license/passport you'll receive an on-the-spot fine of €400! So don't forget to keep that with you wherever you go in the car. All driving licences are valid here, European or not.
There's often a "hidden extra" charge called SCWD or "Super Collision Waiver Damage" so make sure the insurance you have covers absolutely everything. If the SCWD is optional and you don't take it you're liable for the first €300 - €500 of any damage or scratches incurred and the main insurance kicks in after that's paid.
Driving is on the right hand side of the road, with speed limits and warning signs very well marked wherever you go. Buses and taxis always expect you to give way to them and it's a good idea to do this if you like driving safely! Parking anywhere around the resorts is easy to find and often free. If you want to park in the very center of a resort you'll probably find blue lines/markings which means "pay and display" so look for the ticket machine.
If you're planning a trip to the capital, Las Palmas, you'll have to look hard to find a free space, the multi-storey car parks are your best bet and be warned, there is one car to every two people in the city so it gets busy.
The motorway ("GC1") on the east side of the island will take you easily and quickly to Mogan, Puerto Rico, Maspalomas, Playa del Inglés, San Agustín, Las Palmas and the airport. (Airport to Mogan in roughly 45 minutes). It has also been extended to cover the north coast of the island. (GC2) The roads on the west side and those through the centre of the island are minor roads, narrow and windy in parts, so plan longer journey times there. These are also the most scenic routes around the island. Highly recommended is a drive into the mountains towards the village of Tejeda and its national park. Located on Gran Canaria's highest mountain, Cruz de Tejeda (2,000m) The best route into or from the mountains is either from the west, passing through the town of Mogán and from the south where you join the road to San Bartolome de Tirajana at Maspalomas.
To surmise then, there really is a lot to see all around the island. Small as it is, the roads can be narrow and windy so it can take a good 3 days of day-trips to see all of the island, though I highly recommend it. Car hire can often work out to be a much better alternative to seing the island than the holiday "excursions" you are offered by your holidays rep. As well as working out less expensive, you're free to stop off where you want, when you want and for as long as you want.
Note - Getting here from the airport is pretty easy if your car hire starts up there. Leave the airport following the blue signs the say "Sur" (south). This brings you on to the GC1 motorway. San Agustin (first) Playa del Ingles (second) and Maspalomas, Puerto Rico, Taurito & Mogan all have clear exits marked.