Residents need an Emirates ID and a UAE licence. Visitors need a passport, a visa page, and either an international permit or a licence from an exempt country.
There are two versions of this answer and the one that applies to you depends on your residency, not your nationality. UAE residents hire on an Emirates ID and a UAE driving licence. Visitors hire on a passport, the visa or entry stamp, and the licence issued by their own country.
The part that catches people out is the international driving permit. Whether you need one depends entirely on which country issued your licence. Holders from the GCC states and from a long list that includes the UK, the US, Canada, Australia, Japan, South Korea and most of the EU can drive here on their national licence alone. Everyone else needs an IDP alongside it.
The card matters as much as the licence
Every hire needs a credit card in the main driver's name. The security deposit is placed as a hold against the available limit, not taken as a payment, and it is released after the car comes back and any fines have cleared. Debit cards are usually declined for this because a hold cannot be placed on them reliably.
Anyone else who will drive has to be named on the agreement and present the same documents. An unnamed driver is not covered, and that is not a paperwork technicality — it is the difference between a claim being paid and being refused.
An international permit is issued by the country that issued your licence. You cannot get one here for a foreign licence, so sort it out before you fly.