Cars in the United Arab Emirates drive on the right hand side of the road with overtaking on the left. Remaining aware at all times is vital in the UAE as local drivers have a reputation for being fast and reckless and often you'll find yourself overtaken on both sides. Because of this the Emirates have some of the world's highest accident and driving death rates.
Avoiding the rush hours in the cities as much as possible is a good idea as this is when people are at their most volatile.
If you plan to see the incredible deserts surrounding the UAE then choose a 4x4 vehicle. Other safety precautions should be taken. Let people know where you are going before you leave, travel in a convoy of vehicles and always carry lots of food and water with you.
Having a good map is very useful but constant road works mean they rarely stay up-to-date. You may wish to get a GPS to be on the safe side.