The UAE's telephone company, Etisalat, offer a pre-paid
mobile phone service called Wasel. You can obtain your SIM card immediately
from any Etisalat office by presenting your passport and paying a small fee
(the page of your passport with your UAE visa on it will be copied).
Cards to add call credit to your mobile phone are available in petrol stations
and supermarkets. You can also add credit to your account using the machines
provided by Etisalat in large shopping centres. The SIM card is valid for one
year only, after which you will need to renew it if you want to continue using
the same number.
The Wasel plan also provides international roaming,
so you will be able to use your mobile phone outside Dubai.
More information is available on the Etisalat
website, in the Travellers > Visitors section.