As a result of the recent bombings in Erbil the immigration procedures have changed a lot. My employer hires several high profile well connected lawyers to handle all of these issues related to work visas and residencies.
Certain countries can obtain a 15 day free visa upon airport arrival. Then it is necessary to start the procedures. There are fines for overstaying the visa.
Erbil requires complete medical testing which varies depending upon your country of origin. You visit the governmental clinic for the testing and pay for it yourself. They run blood work for aids/HIV, different types of hepatitis, etc. Some people, depending upon their country of origin have to also prove negative for malaria, liver flukes, TB, etc. If you test positive for any of those things you will be denied the permit/visa. They give the results in a public way so it was quite humiliating for a foreign worker, who was not with our group, but was told he tested positive for HIV in front of everyone in the waiting room!!!
The next step (a new one) is an interview at the police station where they ask you many personal questions.
Then if everything is in order you report to the residency office with the results of your Kurdistan Police check, government medical reports, and necessary paperwork filled out by your lawyer.
Work permits/residency permits are valid for 1 year only so the process restarts each year.
Not sure if what I describe above is everyone's experience but it has been mine for the past 4 years with the exception of the police interview which is brand new since the bombings.
You will need all the connections you can get here so be sure to hire someone to help expedite the process. Good luck.