Well, the market is back almost to normal, but most of the jobs in the fields that you are specialized in goes to people who have experience in the filed. I am not trying to kill your enthusiasm, on the contrary, its all in the way we push ourselves.
I am going to choose one area of work here also a country, in general though, these tips can be applied to any job in any country.
Here is my strategy if I am looking for a construction and civil engineering job:
1. prepare a great CV and few reference letters that match the jobs you are applying for. Also prepare a good portfolio of the work that you did while studying. Companies like it that you are prepared. Also don’t forget to say everything about yourself including the little award that you received in first grade for drawing the best palm tree (metaphorically speaking)
2. buy a nice suit.
3. find the companies that are in UAE with background of construction and civil engineering (Google is your best friend here) see if they have vacancies on their websites and apply. Also group the jobs and go visit the companies yourself.
4. check out the jobs on the recruitment companies sites, see this http://www.gulftalent.com/home/jobs-in-Engineering-Civil-Construction-1.html
5. check Linkedin, I am sure you have an account there, http://www.linkedin.com/csearch/results?type=companies&keywords=construction+companies+uae&pplSearchOrigin=GLHD&pageKey=fcs_results&search=Search
6. look at the classified section of the newspapers
7. if all doesn't work in UAE, then try Qatar as its Dubai ten years ago, lots of jobs.