I could not find specific instructions for starting a nonprofit organization in the United Arab Emirates but I did find some information to get you started.

Idealist.org has these suggestions for starting a nonprofit organization:
1. Learn about the United Arab Emirates.
2. Register with the local government agency that handles new “nongovernmental organizations.”
3. Get the local community involved. According to Idealist, All “outside funders”—foundations, government agencies, corporate contributors, major donors—will want to see evidence that the community is involved in, and supports, the plan for the new organization. Develop a strategy for earning income from people who can help pay for the services they receive.
4. Keep good records, watch revenues and expenditures carefully, and be committed to thoughtful planning about when and how to grow. Treat your nonprofit as a business.

I found a great website about starting an NGO http://www.gdrc.org/ngo/start-ngo/index.html
Some key steps include:
1. Check to see if the proposed name of the organization is already in use.
2. Registering or incorporating within your local government. "A typical set of documents to be submitted to the appropriate authority
for registering an NGO includes - Memorandum of Association or
Bye-laws, including applicable rules and regulations; report of annual
activities, financial reports/audit reports; sources and pattern of
income and expenditure; minutes of the Executive Board or General
Assembly that endorses the setting up of the NGO; letters of support
(references) etc."
3.  Fund raise.
4. File for tax exemption with the national tax authority.
5. Develop a constitution/bylaws. This includes: (a) number of members, term length, nomination process, committees, and
meetings; (b) fiscal year/accounting cycles, committees, and officers'
responsibilities; (c) methodologies, tools, and strategies, monitoring
and evaluation etc.; and (d) how to amend the bylaws themselves.

6. Hire staff (and/or find volunteers) and buy office supplies.
7. Insure the organization.

This website has specific information for starting a business in the United Arab Emirates: http://www.doingbusiness.org/ExploreTopics/StartingBusiness/Details.aspx?economyid=195

This website offers a list of United Arab Emirates Charities and Non-Profit Organizations: http://el.hct.ac.ae/regional/uae/charities.htm

Here's a list of Attorneys, Lawyers & Law Firms Nonprofit Organizations in Dubai, United Arab Emirates: http://el.hct.ac.ae/regional/uae/charities.htm

Here is a list of nonprofit resources:
http://www.idealist.org/tools/tools.html

Here is a list of available jobs in nonprofit organizations in the United Arab Emirates: http://www.alluaejobs.com/all_nonprofit_ngo_charity_aid_organization_jobs_in_united_arab_emirates_middle_east_576.html

You can learn more about the United Arab Emirates here: http://www.internationalist.com/redir/?n=http://lcweb2.loc.gov/frd/cs/aetoc.html

Hope this helps!