Once you get your residence visa, you then must get a UAE driving licence. (In other words, it is against the law to drive without one if you have a residence visa.)
A friend of mine called Paul told me that his wife got her residence visa the other day, so today he went with her to get a UAE driving licence for her.
He said the process took 6.5 hours from 9am this morning. Ouch!
Go to the Al Jimi area to get fingerprinted, palm printed and photographed for a UAE Identity Card. You will be given a receipt which you can then take to the traffic department to get a UAE driving licence. (Your Identity Card will be likely be delivered to you by motorcycle courier about 2 weeks later.)
Have your eyes tested at the traffic department. This is the only test you will need to undertake.
I will post all the steps once Paul has read my summary above of what I remember from our chat, and he has got back to me with more info.