A really good way to start is to look online. You need to wait until you have all of the documents below before you buy a car.
Buying using cash/credit card
Financing (financing can only be done from a dealer)
Salik
Salik is basically the toll system used on Sheikh Zayed Road. There are four gates around Dubai which you have to pay AED4 every time you pass them. Rather than having toll booths, it automatically reads the chip in your Salik tag and deducts it from your prepaid account. Once you have purchased your car you must immediately go and buy a Salik tag available from any fuel station otherwise you will be fined. You then have to stick it on the inside of the windscreen and register. Go to http://www.salik.gov.ae/en for more information.