The figures
@Martin Everson put out where mostly correct:
GoFreelance
AED 7,500 Permit (Annually)
AED 2,000 Establishment Card (Annually)
AED 3,900 Residency Visa (3 years incl. Medical Test, Visa Stamping, Emirates ID Card)
AED 10,000 Private Health Insurance (Annually)
AED 17,000 Studio Apartment (Annual Cost)
I put the last two in bold as if you don't plan to actually live in the UAE you can get a basic insurance like Orient for 920 Dirham a year ( a little more than 200 dollar ) and then you can have one insurance like Foyer Global Healt as you real insurance, which will cost you around 1700 Euro each year, and for the Ejari which you need as a proof of residence for opening the bank account you can make an agreement with someone, pay three months of rent up front, keep the contract valid for the time it itakes to open the account and then close the contract. One thing that I always point out, if you move your residence from your home country to Dubai you will probably be under a lot of scrutiny, so act accordingly.